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The ranking of nodes in a network according to their centrality or ''importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The COVID-19 pandemic has recently rejuvenated the interest in this problem, as the ranking may be used to decide who should be tested, or vaccinated, first, in a population of asymptomatic individuals. In this paper, we review classic methods for node ranking and compare their performance in a benchmark network that considers the community-based structure of society. The outcome of the ranking procedure is then used to decide which individuals should be tested, and possibly quarantined, first. Finally, we also review the extension of these ranking methods to weighted graphs and explore the importance of weights in a contact network by providing a toy model and comparing node rankings for this case in the context of disease spread. [ABSTRACT FROM AUTHOR]

Complex systems that consist of diverse kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein product to model this type of networks. Several centrality measures, that are well known for single-layer networks, are extended to multilayer networks using tensors and their properties are investigated. In particular, subgraph centrality based on the exponential and resolvent of a tensor are considered. Krylov subspace methods based on the tensor format are introduced for computing approximations of different measures for large multilayer networks. [ABSTRACT FROM AUTHOR]

The nonzero component graph of a finite-dimensional vector space over a finite field is a graph whose vertices are the nonzero vectors in the vector space, and any two vertices are adjacent if the corresponding linear combination contains a common basis vector. In this paper, we discuss the centrality measures and entropy of the nonzero component graph and also analyze the sensitivity of the graph using the centrality measures. [ABSTRACT FROM AUTHOR]

Many object‐oriented metrics have been proposed in the literature to measure various structural properties of object‐oriented software. Furthermore, many centrality measures have been introduced to identify central nodes in large networks. However, few studies have used them to measure dependencies in software systems. In fact, centrality measures, as opposed to most traditional object‐oriented metrics that mainly focus on intrinsic properties of classes, can be used to better model the control flow and to identify the most important classes in a software system. This paper aims (1) to investigate the relationships between object‐oriented metrics and centrality measures and (2) to explore the ability of their combination to support fault‐proneness prediction from different perspectives (fault‐prone classes, fault severity, and number of faults). Many studies in the literature have addressed the prediction of fault‐prone classes, from different perspectives, using object‐oriented metrics. The main motivation here is in fact to investigate if the information captured by centrality measures is related to fault proneness and complementary to the information captured by object‐oriented metrics and to investigate if the combination of object‐oriented metrics and centrality measures improves the performance of fault‐proneness prediction significantly. We used size, complexity, and coupling object‐oriented metrics in addition to various centrality measures. We collected data from 20 different versions of five open‐source Java software systems. We first studied the relationships between selected metrics and their relationships to fault proneness. Then, we built different models to predict fault‐prone classes using several machine learning algorithms. In addition, we built models to predict if a class contains a high severity fault, and the number of faults in a class. Results indicate that using centrality measures in combination with object‐oriented metrics improves the prediction of fault‐prone classes as well as the prediction of the number of faults in a class. However, the combination has no significant impact, according to the data we collected, on the quality of the prediction of fault severity. Moreover, using centrality measures in combination with object‐oriented metrics also improves the prediction performance of fault proneness and the number of faults in both cross‐version and cross‐system validation. [ABSTRACT FROM AUTHOR]

Dialogic education advocates varied forms of interactional management by teachers. In the context of whole-class discussions, teachers are encouraged to both prompt student involvement through direct mediation, and "step back" to give students a greater sense of agency and responsibility for turn-taking when appropiate. However, it is methodologically challenging to capture the relation between teacher–student and student–student interactions through dialogue in whole-class contexts. One perspective that is especially designed for exploring complex relations in social networks but not as commonly used in dialogic education is social network analysis (SNA). Drawing on 35 whole-class discussion episodes derived from lower secondary classrooms in Norway, this study uses SNA to explore interactional patterns. Methodologically, the study provides novel examples of how SNA can be used both alone and in conjunction with the indicators of interactional productivity to describe the relation between teacher–student and student–student interactions in whole-class discussions. Empirically, a key finding is that an increase in students responding directly to each other in a student-to-student fashion is associated with a reduction in the distribution of productive interactions through dialogue. Theoretically, the study directs attention to the complexities and tensions inherent in key models and concepts in dialogic education. [ABSTRACT FROM AUTHOR]

Competitive bidding in design-bid-build contracts holds the potential to lower bid prices, maximize project outcomes, and promote growth in the construction industry. However, these potential benefits of competitive bidding are contingent upon adequate competition among bidders. State highway agencies (SHAs) traditionally evaluate competition levels predominantly based on the number of bidders, neglecting other key elements such as bidders' competitiveness. Moreover, little research focuses on addressing this limitation. This study proposes a novel data-driven network theory approach to measure competition from the owners' perspective. Specifically, competition is modeled as a bidirected network of connected bidders using their past winning and losing records. We propose different measures of contractors to provide unique insights into the competitiveness of the bidders. These centrality measures are further correlated with the bidding performance using Spearman's rank correlation coefficient. Our findings demonstrate that these proposed centrality measures bear stronger correlations with bidding performance than the number of bidders. By employing this novel approach, SHAs can better understand contractor competitiveness and competition levels during the project-letting phase. [ABSTRACT FROM AUTHOR]

Graph theory is a branch of mathematics that is crucial to modelling applicable systems and networks using matrix representations. In this article, a novel graph-theoretic model was used to assess an urban water distribution system (WDS) in Saudi Arabia. This graph model is based on representing its elements through nodes and links using a weighted adjacency matrix. The nodes represent the points where there can be a water input or output (sources, treatment plants, tanks, reservoirs, consumers, connections), and links represent the edges of the graph that carry water from one node to another (pipes, pumps, valves). Four WDS benchmarks, pumps, tanks, reservoirs, and external sources were used to validate the framework at first. This validation showed that the worst-case scenarios for vulnerability were provided by the fault sequence iterating the calculation of the centrality measurements. The vulnerability framework's application to the Saudi Arabian WDS enabled the identification of the system's most vulnerable junctions and zones. As anticipated, the regions with the fewest reservoirs were most at risk from unmet demand, indicating that this system is vulnerable to the removal of junctions and pipes that are intricately associated with their neighbours. Different centrality metrics were computed, from which the betweenness centrality offered the worst vulnerability prediction measures. The aspects and zones of the WDS that can more significantly impact the water supply in the event of a failure were identified by the vulnerability framework utilising attack tactics. [ABSTRACT FROM AUTHOR]

The current biodiversity crisis requires efficient approaches to address the ongoing impoverishment of natural communities and the depletion of ecosystem services and functions. In this sense, identifying key species that promote the functioning of ecological processes can be strategic to guide actions aiming at the conservation and restoration of biodiversity. Node‐level metrics in interaction networks can be helpful to identify those key species, as they measure the role each species plays in organizing the interactions. Moreover, ecological correlates of species structural roles may vary between local and global networks of interactions, reflecting distinct mechanisms acting at different spatial scales. By studying local seed dispersal networks and one global meta‐network combining those local networks, Moulatlet et al. identified the most important traits explaining bird species centrality at varying spatial scales. They found that body mass was the main trait explaining centrality at the local scale, whereas range size was the main predictor of species centrality at the global scale. In this contribution, besides assessing local interaction networks, Moulatlet et al. adopt a biogeographical perspective to seed dispersal systems, extending our knowledge about the possible mechanisms that underlie the organization of interacting assemblages when changing the spatial scale of observation. Future efforts on this field could include an intermediate scale, comprising the level of metacommunities, shedding light on the interplay between local and spatial processes, both embedded in biogeographical realms, when determining the organization of interactions and the ecological correlates of species roles. [ABSTRACT FROM AUTHOR]

Social media needs social networks to disseminate information among the people who like to interact with each other. Identification of the most prominent influencers is a crucial problem for influence diffusion in applications like viral marketing. Most of the previous works on influence diffusion studied the topological nature of the users but ignored the effects of communities within a network. This paper proposes a new method called the TSGC method, where the whole graph is divided into different non-overlapping communities. Each of the communities is taken as a subgraph by ignoring the connecting links between them. The most influential users are identified by using each node's local and global centrality measures in the given subgraph of a graph. Finally, the ranking of each node is performed by calculating the I s c o r e p of each node within a whole network. Experimental results on six datasets confirm that the proposed TSGC method outperforms many well-known existing methods in terms of influence diffusion phenomenon under both the LT and IC models. This paper also proposes a new model where an active promoter may lose his influencing potential over time, go to a recovered state where he is no longer active or can activate others, and then go to a susceptible state where he is prone to getting influenced in the future. A user who is influenced by an active user can also become an active user. We termed this model the ICIRS model. This model undergoes influence diffusion in continuous time, unlike discrete-time steps as focused in most of the existing papers. Our experimental evaluations on the datasets reveal that the ICIRS model performs non-progressive influence diffusion. [ABSTRACT FROM AUTHOR]

The ranking of nodes in a network according to their centrality or ``importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The COVID-19 pandemic has recently rejuvenated the interest in this problem, as the ranking may be used to decide who should be tested, or vaccinated, first, in a population of asymptomatic individuals. In this paper, we review classic methods for node ranking and compare their performance in a benchmark network that considers the community-based structure of society. The outcome of the ranking procedure is then used to decide which individuals should be tested, and possibly quarantined, first. Finally, we also review the extension of these ranking methods to weighted graphs and explore the importance of weights in a contact network by providing a toy model and comparing node rankings for this case in the context of disease spread. [ABSTRACT FROM AUTHOR]

Background: Spatial ability (SA) was shown to be important for success in different fields, including STEM. Recent research suggested that SA is a unitary construct, rather than a set of related skills. However, it is not clear how individual differences in different facets of SA emerge, and how they relate to variance in general cognitive ability. Aims: The aim of the present study was threefold: 1) to examine the structure of SA testing nine theoretical models; 2) to explore the relation between 16 different facets of SA with general cognitive ability; and 3) to identify central facet(s) within the network of SA – with most links and/or strongest links to other facets. Sample: The study participants were 958 university students from Russia. Methods: The study used a comprehensive battery of 16 SA tests and a verbal ability measure. Results: Results supported previous research, suggesting moderate overlap between all SA facets. Factor analysis suggested several potential structures, with similar fit indices for five different theoretically driven models, including split into small‐ and large scale; partially independent manipulation, visualization and navigation facets. Confirmatory factor analysis, mediation and network analyses showed spatial ability being largely independent from verbal ability. In addition, network analysis showed that navigation according to directions is in the centre of the network, potentially linking all SA facets. Conclusion: The results have potential implications for identifying the best targets for SA interventions. The next step in research is conducting experimental studies to evaluate effectiveness of interventions targeting navigation in comparison with other facets of SA. [ABSTRACT FROM AUTHOR]

Simple Summary: Small-scale systems are the most widespread productive system in developing countries. However, these systems have historically suffered from a low technological level, which constitutes their main problem and endangers the maintenance of the system and rural people who depend for their livelihood on it. Therefore, deepening the knowledge of the technology adoption process is key to its improvement, as well as including a gender approach to develop more effective public policies. In this research, very small commercial farms with a similar structure and size in the Mexican tropics (n = 383) were analysed, and the Social Network Analysis (SNA) was used to identify technology adoption patterns among male and female farmers of dual-purpose cattle. Five technological packages were analysed and statistically significant differences were found between genders in the area of reproduction. The results have shown that women even when not occupying central positions, are close to the leaders in the network, quickly adopting the re-productive technologies the leaders selected. Furthermore, farms run by women were smaller although with greater specialization and milk productivity, increasing productivity by 20%. This paper examines the role of women in the dual-purpose livestock system (DP) in Mexico through their technological adoption patterns and aims to evaluate whether there are significant differences between the technology adoption networks of men and women farmers. The sample was composed of 383 DP small farms with 20 or fewer cows and a high level of vulnerability. Social Network Analysis (SNA) was applied, and the centrality measures were calculated for the technological areas of management, feeding, genetics, reproduction, and animal health. Significant differences were found in reproduction levels between men and women farmers. Therefore, SNA was developed in this technological area where men mainly occupied central positions (brokers) while women were just close to the leaders in the network. The results have shown that farms run by women were smaller and presented higher levels of specialization and milk productivity (20% higher), and women prioritized those technologies linked to female reproductive efficiency. Moreover, women were deeply embedded in men's networks through numerous ties and were capable of building connections with groups of farmers outside of their own group. [ABSTRACT FROM AUTHOR]

Dialogic education advocates varied forms of interactional management by teachers. In the context of whole-class discussions, teachers are encouraged to both prompt student involvement through direct mediation, and “step back” to give students a greater sense of agency and responsibility for turn-taking when appropiate. However, it is methodologically challenging to capture the relation between teacher–student and student–student interactions through dialogue in whole-class contexts. One perspective that is especially designed for exploring complex relations in social networks but not as commonly used in dialogic education is social network analysis (SNA). Drawing on 35 whole-class discussion episodes derived from lower secondary classrooms in Norway, this study uses SNA to explore interactional patterns. Methodologically, the study provides novel examples of how SNA can be used both alone and in conjunction with the indicators of interactional productivity to describe the relation between teacher–student and student–student interactions in whole-class discussions. Empirically, a key finding is that an increase in students responding directly to each other in a student-to-student fashion is associated with a reduction in the distribution of productive interactions through dialogue. Theoretically, the study directs attention to the complexities and tensions inherent in key models and concepts in dialogic education. [ABSTRACT FROM AUTHOR]

Modelling interactions on complex networks needs efficient algorithms for describing processes on a detailed level in the network structure. This kind of modelling enables more realistic applications of spreading processes, network metrics, and analyses of communities. However, different real-world processes may impose requirements for implementations and their efficiency. We discuss different transmission and spreading processes and their interrelations. Two pseudo-algorithms are presented, one for the complex contagion spreading mechanism using non-self-avoiding paths in the modelling, and one for simple contagion processes using self-avoiding paths in the modelling. The first algorithm is an efficient implementation that can be used for describing social interaction in a social network structure. The second algorithm is a less efficient implementation for describing specific forms of information transmission and epidemic spreading. [ABSTRACT FROM AUTHOR]

The aftermath of including new technologies in a modern electric system in conjunction with the incessant rise in power demand could pose a risk to the optimal operation of the system. Therefore, it becomes imperative to identify the most influential and critical nodes of such a system to avert future problems in network operation. In this paper, to identify most significant nodes of the system, the authors propose two measures of centrality in accordance with the network structural properties of a power system, namely, degree centrality (DC) and eigenvector centrality (EC). These are expressed considering the admittance matrix that exists among the interconnection of load to load nodes in an electrical power network. A critical node closeness centrality (CNCC) method is also proposed to identify critical nodes of the system. This is done by modifying the conventional closeness centrality (CC) to include the influence of interconnection that exists between network load to load nodes as captured by the admittance matrix between them. A comparative analysis of the proposed techniques with other conventional methods is also carried out. The result of the simulation shows that the proposed methods could serve as alternative tools in the identification of influential and weak nodes in a power system. [ABSTRACT FROM AUTHOR]

The enhancement of Robustness (R) has gained significant importance in Scale-Free Networks (SFNs) over the past few years. SFNs are resilient to Random Attacks (RAs). However, these networks are prone to Malicious Attacks (MAs). This study aims to construct a robust network against MAs. An Intelligent Rewiring (INTR) mechanism is proposed to optimize the network R against MAs. In this mechanism, edge rewiring is performed between the high and low degree nodes to make a robust network. The Closeness Centrality (CC) measure is utilized to determine the central nodes in the network. Based on the measure, MAs are performed on nodes to damage the network. Therefore, the connections of the neighboring nodes in the network are greatly affected by removing the central nodes. To analyze the network connectivity against the removal of nodes, the performance of CC is found to be more efficient in terms of computational time as compared to Betweenness Centrality (BC) and Eigenvector Centrality (EC). In addition, the Recalculated High Degree based Link Attacks (RHDLA) and the High Degree based Link Attacks (HDLA) are performed to affect the network connectivity. Using the local information of SFN, these attacks damage the vital portion of the network. The INTR outperforms Simulated Annealing (SA) and ROSE in terms of R by 17.8% and 10.7%, respectively. During the rewiring mechanism, the distribution of nodes' degrees remains constant. [ABSTRACT FROM AUTHOR]

The behaviour of individual users in an online social network is a major contributing factor in determining the outcome of multiple network phenomenon. Group formation, growth of the network, information propagation, and rumour blocking are some of the many network behavioural traits that are influenced by the interaction patterns of the users in the network. Network motifs capture one such interaction pattern between users in online social networks (OSNs). For this work, four second-order (two-edged) network motifs have been considered, namely, message receiving pattern, message broadcasting pattern, message passing pattern, and reciprocal message pattern, to analyse user behaviour in online social networks. This work provides and utilizes a node interaction pattern-finding algorithm to identify the frequency of aforementioned second-order network motifs in six real-life online social networks (Facebook, GPlus, GNU, Twitter, Enron Email, and Wiki-vote). The frequency of network motifs participated in by a node is considered for the relative ranking of all nodes in the online social networks. The highest-rated nodes are considered seeds for information propagation. The performance of using network motifs for ranking nodes as seeds for information propagation is validated using statistical metrics Z-score, concentration, and significance profile and compared with baseline ranking methods in-degree centrality, out-degree centrality, closeness centrality, and PageRank. The comparative study shows the performance of centrality measures to be similar or better than second-order network motifs as seed nodes in information diffusion. The experimental results on finding frequencies and importance of different interaction patterns provide insights on the significance and representation of each such interaction pattern and how it varies from network to network. [ABSTRACT FROM AUTHOR]

• Neoteric representation of biological networks by weighted directed hypergraph. • Identification of influential nodes using weak tie of directed hypergraph. • Hybridisation of degree centralities with genetic algorithm for optimizing the weights. • Reduced complexity by means of much lesser hyperedges compared to edges and compared results with graph centrality measures. • Influential COVID-19 proteins are identified from protein interactions which could be used for drug design. Network structures have attracted much interest and have been rigorously studied in the past two decades. Researchers used many mathematical tools to represent these networks, and in recent days, hypergraphs play a vital role in this analysis. This paper presents an efficient technique to find the influential nodes using centrality measure of weighted directed hypergraph. Genetic Algorithm is exploited for tuning the weights of the node in the weighted directed hypergraph through which the characterization of the strength of the nodes, such as strong and weak ties by statistical measurements (mean, standard deviation, and quartiles) is identified effectively. Also, the proposed work is applied to various biological networks for identification of influential nodes and results shows the prominence the work over the existing measures. Furthermore, the technique has been applied to COVID-19 viral protein interactions. The proposed algorithm identified some critical human proteins that belong to the enzymes TMPRSS2, ACE2, and AT-II, which have a considerable role in hosting COVID-19 viral proteins and causes for various types of diseases. Hence these proteins can be targeted in drug design for an effective therapeutic against COVID-19. [ABSTRACT FROM AUTHOR]

The rising number of users and the demand for more diverse and specialized applications have led to a tremendous increase in network traffic. Managing diverse traffic demands from numerous applications is a challenging task for the existing traditional networking architecture. Hybrid software defined network is widely used to simplify operations providing flexible traffic management and automation. However, managing dynamic traffic demands and routing traffic flows is a challenging task. Therefore, in this paper, a centrality based Q-learning routing traffic engineering method for congestion detection and optimized traffic routing is proposed. The proposed method uses the reinforcement Q-learning algorithm to find an optimal path for routing the traffic. The centrality measures of the nodes are computed and ranked using the simple additive weighted method to detect the top k high-risk nodes. Simulations are carried out under different network scenarios for various traffic profiles. The results show that the proposed method outperformed the existing methods in terms of path length, delay, link utilization, throughput and computation time. [ABSTRACT FROM AUTHOR]

Objectives: We investigate the spatio-temporal variation of monthly residential burglary frequencies across neighborhoods as a function of crime generators, street network features and temporally and spatially lagged burglary frequencies. In addition, we evaluate the performance of the model as a forecasting tool. Methods: We analyze 48 months of police-recorded residential burglaries across 20 neighborhoods in Amsterdam, the Netherlands, in combination with data on the locations of urban facilities (crime generators), frequencies of other crime types, and street network data. We apply the Integrated Laplace Approximation method, a Bayesian forecasting framework that is less computationally demanding than prior frameworks. Results: The local number of retail stores, the number of street robberies perpetrated and the closeness of the local street network are positively related to residential burglary. Inclusion of a general spatio-temporal interaction component significantly improves forecasting performance, but inclusion of spatial proximity or temporal recency components does not. Discussion: Our findings on crime generators and street network characteristics support evidence in the literature on environmental correlates of burglary. The significance of spatio-temporal interaction indicates that residential burglary is spatio-temporally concentrated. Our finding that recency and proximity of prior burglaries do not contribute to the performance of the forecast, probably indicates that relevant spatio-temporal interaction is limited to fine-grained spatial and temporal units of analysis, such as days and street blocks. [ABSTRACT FROM AUTHOR]

Despite a plethora of centrality measures were proposed, there is no consensus on what centrality is exactly due to the shortcomings each measure has. In this manuscript, we propose to combine centrality measures pertinent to a network by forming their convex combinations. We found that some combinations, induced by regular points, split the nodes into the largest number of classes by their rankings. Moreover, regular points are found with probability 1 and their induced rankings are insensitive to small variation. By contrast, combinations induced by critical points are scarce, but their presence enables the variation in node rankings. We also discuss how optimum combinations could be chosen, while proving various properties of the convex combinations of centrality measures. [ABSTRACT FROM AUTHOR]

Network cascades represent a number of real-life applications: social influence, electrical grid failures, viral spread, and so on. The commonality between these phenomena is that they begin from a set of seed nodes and spread to other regions of the network. We consider a variant of a critical node detection problem dubbed the robust critical node fortification problem, wherein the decision maker wishes to fortify nodes (within a budget) to limit the spread of cascading behavior under uncertain conditions. In particular, the arc weights—how much influence one node has on another in the cascade process—are uncertain but are known to lie in some range bounded by a worst-case budget uncertainty. This problem is shown to be N P -hard even in the deterministic case. We formulate a mixed-integer program (MIP) to solve the deterministic problem and improve its continuous relaxation via nonlinear constraints and convexification. The robust problem is computationally more difficult, and we present an MIP-based expand-and-cut exact solution algorithm, in which the expansion is enhanced by cutting planes, which are themselves tied to the expansion process. Insights from these exact solutions motivate two novel (interrelated) centrality measures, and a centrality-based heuristic that obtains high-quality solutions within a few seconds. Finally, extensive computational results are given to validate our theoretical developments as well as provide insights into structural properties of the robust problem and its solution. [ABSTRACT FROM AUTHOR]

The purpose of the study is to use a social network analysis of a construction project's participants to identify key participants using centrality measures and identify communities of participants in the network. This article analyses the communication network of a construction project that consists of 34 participants. Analysis of four centrality measures of the network's nodes showed that there was a significant information load for a few key participants. The Eigenvector Centrality was chosen as the most appropriate basic measure of centrality because it takes into account the neighbouring nodes' level of importance. The Louvain clustering method was found to be more effective than the Girvan–Newman method. The Louvain algorithm divided the project communication network into three communities, in which the participants are interconnected by the technological processes and the work performed. A hypothetical example is presented of how the clustering technique can be used to improve project communication. Adding a 'Project Manager Assistant' was selected for addition, and assumptions made to demonstrate how the load might be reduced and effectiveness assessed. These methods of assessing centrality and clustering show potential in project management to analyse a real communication network and when making managerial decisions. [ABSTRACT FROM AUTHOR]

Researchers worldwide are striving hard to find a solution for the coronavirus pandemic and reduce the fatalities from this severe outbreak. The purpose of this article is to evaluate and visualize the published documents about coronavirus research, based on extracted data from Web of Science (WoS) citation database. The study used a bibliometric method and social network analysis. Data were collected using the WoS database on February 23, 2020, with 13252 records being retrieved and used as the study sample. Descriptive statistics were used in the bibliometric method and network analysis. Text Statistics Analyzer and ISI.exe were used to compute the number of authors per document. VOSviewer and UCINET were used respectively for visualization and for measuring the centrality and the density of networks. Study findings indicate the top actors of the scientific society (authors, institutions, countries) that had the most publication on coronavirus. Similarly, the top keywords used by authors were identified. Also, the density and centrality measures of co-authorship networks (degree, closeness, betweenness) for the top 10 authors, institutions, countries, and keywords were identified. The Journal of Virology had the highest number of published papers on coronavirus research. The study revealed that the leading researchers and institutions were mostly from the United States of America, England, China, Germany, Netherlands, France, Canada, Japan, South Korea, and Saudi Arabia. [ABSTRACT FROM AUTHOR]

To analyze the structure of social networks, the methods of cooperative game theory can be adopted. One of such methods is based on the calculation of the Myerson values as a centrality measure of the vertices in a graph. In this case, the number of paths of a certain length in the subgraphs corresponding to the coalitions is used as the characteristic function. This paper proposes a modification of the Myerson value for the case where the paths in a graph containing cycles are included in consideration. The effectiveness of this approach is illustrated by several examples. [ABSTRACT FROM AUTHOR]

• The study integrates socio-environmental analysis using urban configuration and landscape ecology models to examine spatial networks in Pelotas, Brazil. • The article discusses the relationship and statistical correlation between urban and ecological networks. • The methodology represents a valuable tool for urban planners and researchers to create and better understand urban green areas. • The methodology is applied in a specific area of Pelotas, Brazil. Urbanization has been expanding rapidly in Brazil, negatively impacting the natural environment. Achieving sustainable development requires understanding the interdependencies between the social and natural worlds and finding a balance between them. Resilient urban planning considering green infrastructure can generate socio-environmental benefits through ecological connections. To achieve this, an integrated study between the social and environmental spheres is required, which are often developed separately. Thus, this investigation aims to develop a socio-environmental analysis by adopting urban configuration and landscape ecology models and subsequently comparing their respective outcomes. To this end, two models of spatial networks were examined in a sector of Pelotas, Brazil, based on graph theory and centrality measures. The urban configuration model was used to analyze human mobility in urban networks, while the landscape ecology model was used to study the butterfly species Heliconius erato phyllis in ecological networks. Our findings show no significant correlation between the outcomes generated by the two models, indicating a lack of cohesion in the location and connection of green infrastructure in the study area. This methodology represents a valuable tool for urban planners and researchers seeking to gain new insights into the performance of urban green areas while considering both human and species-related factors. [ABSTRACT FROM AUTHOR]

In protein interaction networks, a complex is a group of proteins that causes a biological process to take place. The correct identification of complexes can help to better understand function of cells used for therapeutic purposes, such as drug discoveries. This paper uses core-attachment structure, centrality measures, and biological properties of proteins to identify protein complex with the aim of enhancing prediction accuracy compared to related work. We used the inherent organization of complex to the identification in this article, while most methods have not considered such properties. On the other hand, clustering methods, as the common method for identifying complexes in protein interaction networks have been applied. However, we want to propose a method for more accurate identification of complexes in this article. Using this method, we determined the core center of each complex and its attachment proteins using the centrality measures, biological properties and weight density, whereby the weight of each interaction was calculated using the protein information in the gene ontology. In the proposed approach to weighting the network and measuring the importance of proteins, we used our previous work. To compare with other methods, we used datasets DIP, Collins, Krogan, and Human. The results show that the performance of our method was significantly improved, compared to other methods, in terms of detecting the protein complex. Using the p-value concept, we show the biological significance of our predicted complexes. The proposed method could identify an acceptable number of protein complexes, with the highest proportion of biological significance in collaborating on the functional annotation of proteins. [ABSTRACT FROM AUTHOR]

With the widespread application of complex network theory, identifying vital nodes is an important part of complex network analysis, which has been a key issue in analyzing the characteristics of network structure and functions. Although many centrality measures have been proposed to identify vital nodes, there is still a lack of an objective performance testing platform for evaluating vital nodes identification algorithms. This study introduces the complex scheduling network as an objective performance testing platform where the identification of vital nodes directly determines the decision-making in each decision scenario through the development of heuristic algorithms upon centrality measures, and therefore, the optimization goals of scheduling problems can be regarded as an objective index for evaluating vital node identification algorithms. Finally, the undirected network obtained by the open shop scheduling problem is taken as an example to analyze and evaluate the performance of various vital node identification algorithms. [ABSTRACT FROM AUTHOR]

In this paper, some results concerning the PageRank versatility measure for multiplex networks are given. This measure extends to the multiplex setting the well‐known classic PageRank. Particularly, we focus on some spectral properties of the Laplacian matrix of the multiplex and on obtaining boundaries for the ranking value of a given node when some personalization vector is added, as in the classic setting. [ABSTRACT FROM AUTHOR]

Analysis of the terrorist network is a process to analyze or deriving Useful information from the available network data. Ranking The Terrorist nodes within a terrorist network in identifying the most influential node is essential for the elaboration of Covert network mining. The purpose of this paper is to implement an approach of two dimensional criteria weight determination along with logarithmic concept implementation for vital node investigation in term of their influential ability. Betweenness, Closeness, Eigenvector, Hub, In-degree, Inverse closeness, Out-degree and Total degree considered as criteria and terrorist involved in 9/11 terrorist attack considered as alternatives used to formulate a decision problem. Although an integrated approach of Fuzzy based subjective-Aggregation concept based objective criteria weight determination and Ranking alternatives by the implementation of the logarithmic concept is used to solve multi criteria decision problems in order to show the application of most centralized node identification process which can be obtained easily by classification and selection problem solution using multiple criteria and alternatives. [ABSTRACT FROM AUTHOR]

The network approach represents a novel paradigm for exploring relations between psychological constructs and observable variables. According to this approach, variables form an autonomous dynamical system; the psychological construct is therefore not viewed as their common cause, but a result of their complex interactions. From an analytical point of view, this approach is based on network analysis —a set of procedures which models variables as nodes connected by a set of edges. This paper presents an overview of network analytical procedures. In other words, it offers a brief explanation of the methods, as well as their practical application in two separate datasets. The first dataset represents data on DASS-21 (N = 1016) and it serves to demonstrate network estimation, centrality measures calculation, community detection and network stability analyses. According to the results, the highest centrality was obtained for the depression item I felt that I had nothing to look forward to, anxiety item I felt I was close to panic, and stress item I felt that 1 was using a lot of nervous energy. As expected, nodes were grouped into three clusters, namely Depression, Anxiety and Stress. Stability analyses demonstrated limited stability of edge strength, while the stability of node centrality depended on the measure used. In the second dataset, which represents data on adolescents' attitudes towards one's body appearance, the Network Comparison Test was demonstrated by comparing male (n = 524) and female (n = 763) networks. Results showed that the two networks do not differ substantially. [ABSTRACT FROM AUTHOR]

Background: The concept of European psychologisation of depression versus somatisation in non-European populations has been the basis of several studies of cultural psychopathology in the general population. Little is currently known about cross-cultural differences and similarities in late-life depression symptom reporting. We cross-culturally compared symptom reporting in the context of Major Depressive Disorder (MDD) among community-dwelling older adults from Spain and Nigeria.Methods: We relied on data from two household multistage probability samples comprising 3,715 persons aged 65 years or older in the Spanish and Nigerian populations. All participants underwent assessments for MDD using the World Mental Health Survey version of the Composite International Diagnostic Interview. Cross-cultural comparison of broad somatic and psychological categories as well as relationship and influence of individual symptoms were analysed using the Symptom Network Analysis approach.Results: Current MDD was diagnosed in 232 and 195 older persons from Spain and Nigeria, respectively. The symptom network of the two samples were invariant in terms of global strength, S(GSPAIN , GNIGERIA ) = 7.56, P = .06, with psychological and somatic symptoms demonstrating centrality in both countries. However, country-specific relationships and influence of individual symptoms were found in the network structure of both samples, M(GSPAIN , GNIGERIA ) = 2.95, P < .01.Conclusion: Broad somatic and psychological symptoms categories contributed to the structural network of older Africans and their peers from the Spanish population. Variations in the relationship and influence of individual symptoms suggests that the functional and "communicative" role of individual symptoms may be differentiated by context specific imperatives. J Am Geriatr Soc 68:-, 2020. [ABSTRACT FROM AUTHOR]

Earthquake clustering is a significant feature of seismic catalogs, both in time and space. Several methodologies for earthquake cluster identification have been proposed in the literature in order to characterize clustering properties and to analyze background seismicity. We consider two recent data‐driven declustering techniques, one based on nearest‐neighbor distance and the other on a stochastic point process. These two methods use different underlying assumptions and lead to different classifications of earthquakes into background events and clustered events. We investigated the classification similarities by exploiting graph representations of earthquake clusters and tools from network analysis. We found that the two declustering algorithms produce similar partitions of the earthquake catalog into background events and earthquake clusters, but they may differ in the identified topological structure of the clusters. Especially the clusters obtained from the stochastic method have a deeper complexity than the clusters from the nearest‐neighbor method. All of these similarities and differences can be robustly recognized and quantified by the outdegree centrality and closeness centrality measures from network analysis. Plain Language Summary: Clustering, in both space and time, is a widely recognized feature of seismicity. An adequate identification of earthquake clusters allows splitting seismicity into background and clustered events (e.g., aftershocks) and is an essential step in several studies, ranging from seismic hazard assessment to long‐ and short‐term earthquake forecasting. Also, the space‐time patterns of identified clusters may provide useful insights on the structural and dynamic tectonic features of a region. Among the several methods proposed so far to identify and characterize seismic clusters, we consider two recent data‐driven declustering techniques, one based on nearest‐neighbor distance and the other on a stochastic point process. These two methods use different underlying assumptions and may lead to different classifications of earthquakes into background events and clustered events. Therefore, this study aims to compare their performances, including clusters structure characterization, by exploiting tree graph representations and tools from network analysis. We found that (1) the two declustering algorithms produce similar partitions of the earthquake catalog; (2) they may differ in the internal structure outlined for individual clusters, with the nearest‐neighbor method usually providing simpler structures than the stochastic declustering method; and (3) these features can be robustly quantified by centrality measures widely used in network analysis. Key Points: Two recent data‐driven declustering methods are compared, one based on nearest‐neighbor distance and one on the ETAS modelSimilarities in classification and in earthquake clusters are investigated by tree graphs and tools from network analysisObtained clusters are consistent, though nearest‐neighbor method usually provides simpler structures than stochastic declustering method [ABSTRACT FROM AUTHOR]

Technology has continuously been a crucially influenced and acutely tangled with the progress of society. Online Social Networks (OSN) are interesting and valuable datasets that can be leveraged to improve understanding about society and to know inter-personal choices. Identification and Ranking of Influential Nodes (IRIN) is non-trivial task for real time OSN like Twitter which accustom with ever-changing network, demographics and contents having heterogeneous features such as Tweets, Likes, Mentions and Retweets. Existing techniques such as Centrality Measures and Influence Maximization ignores vital information available on OSN, which are inappropriate for IRIN. Most of these approaches have high computational complexity i.e. O (n 3) . This research aims to put forward holistic approach using Heterogeneous Surface Learning Features (HSLF) for IRIN on specific topic and proposes two approaches: Average Consensus Ranking Aggregation and Weighted Average Consensus Ranking Aggregation using HSLF. The effectiveness and efficiency of the proposed approaches are tested and analysed using real world data fetched from Twitter for two topics, Politics and Economy and achieved superior results compared to existing approaches. The empirical analysis validate that the proposed approach is highly scalable with low computational complexity and applicable for large datasets. [ABSTRACT FROM AUTHOR]

This work deals with the issue of assessing the influence of a node in the entire network and in the subnetwork to which it belongs as well, adapting the classical idea of vertex centrality. We provide a general definition of relative vertex centrality measure with respect to the classical one, referred to the whole network. Specifically, we give a decomposition of the relative centrality measure by including also the relative influence of the single node with respect to a given subgraph containing it. The proposed measure of relative centrality is tested in the empirical networks generated by collecting assets of the S & P 100, focusing on two specific centrality indices: betweenness and eigenvector centrality. The analysis is performed in a time perspective, capturing the assets influence, with respect to the characteristics of the analysed measures, in both the entire network and the specific sectors to which the assets belong. [ABSTRACT FROM AUTHOR]

Centrality measures have been helping to explain the behavior of objects, given their relation, in a wide variety of problems, since sociology to chemistry. This work considers these measures to assess the importance of every classifier belonging to an ensemble of classifiers, aiming to improve a Multiple Classifier System (MCS). Assessing the classifier's importance by employing centrality measures, inspired two different approaches: one for selecting classifiers and another for fusion. The selection approach, called Centrality Based Selection (CBS), adopts a trade-off between the classifier's accuracy and their diversity. The sub-optimal selected subset presents good results against selection methods from the literature, being superior in 67.22% of the cases. The second approach, the integration, is named Centrality Based Fusion (CBF). This approach is a weighted combination method, which is superior to literature in 70% of the cases. [ABSTRACT FROM AUTHOR]

Since 9/11, terrorism has become a global issue of the twenty-first century. Terrorist organizations become important actors of world politics as they gain influence on political process and decision-making. Some organizations compete with each other in order to gain more power and influence. We study the distribution of power among terrorist groups using network approach and applying classic and new centrality indices (Short-Range (SRIC) and Long-Range interactions indices (LRIC)). These indices allow to identify terrorist groups with direct and indirect influence on the terrorist network. [ABSTRACT FROM AUTHOR]

Ensemble of classifiers can improve classification accuracy by combining several models. The fusion method plays an important role in the ensemble performance. Usually, a criterion for weighting the decision of each ensemble member is adopted. Frequently, this can be done using some heuristic based on accuracy or confidence. Then, the used fusion rule must consider the established criterion for providing a most reliable ensemble output through a kind of competition among the ensemble members. This article presents a new ensemble fusion method, named centrality score‐based fusion, which uses the centrality concept in the context of social network analysis (SNA) as a criterion for the ensemble decision. Centrality measures have been applied in the SNA to measure the importance of each person inside of a social network, taking into account the relationship of each person with all others. Thus, the idea is to derive the classifier weight considering the overall classifier prominence inside the ensemble network, which reflects the relationships among pairs of classifiers. We hypothesized that the prominent position of a classifier based on its pairwise relationship with the other ensemble members could be its weight in the fusion process. A robust experimental protocol has confirmed that centrality measures represent a promising strategy to weight the classifiers of an ensemble, showing that the proposed fusion method performed well against the literature. [ABSTRACT FROM AUTHOR]

• An approach to inexact graph matching using centrality measures. • Reduce the search space by removing the nodes with least centrality values. • Used degree, betweenness, eigenvector and PageRank centrality for comparison. • Implemented the proposed framework on letter and AIDS dataset. • Experiments show that the proposed method can be used for time vs accuracy trade-off. Graph matching is the task of finding the similarity between the two graphs. Error-tolerant graph matching is the process of computing the similarity between the two graphs, where some flexibility to noise or error is allowed to approximate the value of graph matching. In this paper, we present a framework for graph matching by utilizing the centrality measures to ignore the least central nodes of the graphs. Experimental evaluation shows that this approach can be useful to reduce the overall matching time and it can provide time versus accuracy trade-off. [ABSTRACT FROM AUTHOR]

A cooperative game with transferable utility is a situation in which players can generate worth by cooperating and obtain a certain payoff via a sharing rule. In this paper we assume that the cooperation between players is restricted by an acyclic graph. We introduce new sharing rule for this type of game. We also offer an axiomatization of this sharing rule, based mainly on linearity and a consistency axiom. For unanimity games, this sharing rule identifies the center of the graph. • We introduce a new sharing rule for cooperative games on acyclic graphs. • Its characterization revolves around associated consistency along with other axioms. • All axioms are proved to be logically independent. • This sharing rule offers new results for cooperative games on acyclic graphs. • The results are widely opposed to those of the Myerson value. [ABSTRACT FROM AUTHOR]

Graph parameters and topological indices allow a discussion about hierarchical criteria for ranking monocyclic and polycyclic molecular (constitutional) chemical graphs. For brevity, chemical constitutional graphs will be referred to as CGs. These criteria include the number of vertices (graph order), cyclomatic numbers, vertex degrees (from one to four), number of polygons with increasing numbers of edges (3-, 4-, 5-gons, etc.), and vicinity with vertices of increasing rank. A similar hierarchy can be established for ranking vertices in a CG, and a detailed discussion is presented for ordering vertices in all seven identity CGs with 6 vertices and in 25 from the many identity CGs with 7 vertices. This is the first discussion of ranking the vertices of CGs from the viewpoint of centrality measures. [ABSTRACT FROM AUTHOR]

With the immense growth of scientific literature over the Web, the authors of research papers are being ranked for various purposes such as for being shortlisted for different scientific awards, for prestigious position, for tenured appointments, for keynote speaker invitation or for allocation of research grants. The traditional paradigm to attain these aspects is based on bibliometric indices, such as publication count, citation count and h-index. The quintessential indicator among all these indices are based on a number of citations received by the publication of an author. Generally, when a research paper is published, it receives citations after some time and may take more than a couple of years to attain a reasonable number of received citations which could make a difference in researcher ranking based on bibliometric parameters. Therefore, dependability over these bibliometric indices for authors ranking is not beneficial for researchers at the start of their academic career. Such authors are less likely to have a fair chance to compete with their senior counterparts. This study aims at overcoming the above-mentioned deficiency with the assistance of network centrality measures using the co-author network. The experiments are conducted to rank authors in order to identify the awardees of various scientific societies. The obtained ranking is further evaluated by comparing the results of bibliographic indices and network-based indices. The results revealed that network indices have equal potential to identify influential authors as compared with bibliometric indices such as h-index, particularly in the case of networks having a high value of cluster coefficient. Based on the obtained results, it is observed, awardees that are exclusively identified by network centrality measures are more than 5 years younger as compared to their counterparts who are exclusively identified by bibliometric indices. [ABSTRACT FROM AUTHOR]

This research establishes that many real-world networks exhibit bounded expansion 2 , a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. Specifically, we give a new linear-time fpt algorithm for motif counting and linear time algorithms to compute localized variants of several centrality measures. To establish structural sparsity in real-world networks, we analyze several common network models regarding their structural sparsity. We show that, with high probability, (1) graphs sampled with a prescribed sparse degree sequence; (2) perturbed bounded-degree graphs; (3) stochastic block models with small probabilities; result in graphs of bounded expansion. In contrast, we show that the Kleinberg and the Barabási–Albert model have unbounded expansion. We support our findings with empirical measurements on a corpus of real-world networks. [ABSTRACT FROM AUTHOR]

Complex networks are ubiquitous to several computer science domains. Centrality measures are an important analysis mechanism to uncover vital elements of complex networks. However, these metrics have high computational costs and requirements that hinder their applications in large real-world networks. In this tutorial, we explain how the use of neural network learning algorithms can render the application of the metrics in complex networks of arbitrary size. Moreover, the tutorial describes how to identify the best configuration for neural network training and learning such for tasks, besides presenting an easy way to generate and acquire training data.We do so by means of a general methodology, using complex network models adaptable to any application. We show that a regression model generated by the neural network successfully approximates the metric values and therefore is a robust, effective alternative in real-world applications. The methodology and proposed machine-learning model use only a fraction of time with respect to other approximation algorithms, which is crucial in complex network applications. [ABSTRACT FROM AUTHOR]

Tropospheric ozone ( O 3 ) time series have been converted into complex networks through the recent so-called Visibility Graph (VG), using the data from air quality stations located in the western part of Andalusia (Spain). The aim is to apply this novel method to differentiate the behavior between rural and urban regions when it comes to the ozone dynamics. To do so, some centrality parameters of the resulting complex networks have been investigated: the degree, betweenness and shortest path. Some of them are expected to corroborate previous works in order to support the use of this technique; while others to supply new information. Results coincide when describing the difference that tropospheric ozone exhibits seasonally and geographically. It is seen that ozone behavior is fractal, in accordance to previous works. Also, it has been demonstrated that this methodology is able to characterize the divergence encountered between measurements in urban environments and countryside. In addition to that, the promising outcomes of this technique support the use of complex networks for the study of air pollutants dynamics. Particularly, new nuances are offered such as the identification and description of singularities in the signal. Image 1 [ABSTRACT FROM AUTHOR]

Centrality indices aim to quantify the importance of nodes or edges in a network. Much interest has been recently raised by the body of work in which a node's connectivity is understood less as its contribution to the quality or speed of communication in the network and more as its role in enabling communication altogether. Consequently, a node is assessed based on whether or not the network (or part of it) becomes disconnected if this node is removed. While these new indices deliver promising insights, to date very little is known about their theoretical properties. To address this issue, we propose an axiomatic approach. Specifically, we prove that there exists a unique centrality index satisfying a number of desirable properties. This new index, which we call the Attachment centrality , is equivalent to the Myerson value of a certain graph-restricted game. Building upon our theoretical analysis we show that, while computing the Attachment centrality is #P-complete, it has certain computational properties that are more attractive than the Myerson value for an arbitrary game. In particular, it can be computed in chordal graphs in polynomial time. [ABSTRACT FROM AUTHOR]

Purpose: The development of innovations in all the research and development (R&D) fields is leading to a huge increase of patent data. Therefore, it is reasonable to foresee that, in the next future, Big Data-centered techniques will be compulsory to fully exploit the potential of this kind of data. In this context, network analysis-based approaches are extremely promising. The purpose of this paper is to provide a contribution to this setting. In fact, the authors propose a well-tailored centrality measure for evaluating patents and their citations. Design/methodology/approach: The authors preliminarily introduce a suitable support directed network representing patents and their citations. After this, the authors present the centrality measures, namely, "Naive Patent Degree" and "Refined Patent Degree.'" Then, the authors show why they are well tailored to capture the specificities of the patent scenario and why classical centrality measure fails to fully reach this purpose. Findings: The authors present three possible applications of the measures, namely: the computation of a patent "scope" allowing the evaluation of the width and the strength of the influence of a patent on a given R&D field; the computation of a patent lifecycle; and the detection of the so-called "power patents," i.e., the most relevant patents, and the investigation of the importance, for a patent, to be cited by a power patent. Originality/value: None of the approaches proposing the application of centrality measures to patent citation networks consider the main peculiarity of this scenario, i.e., that, if a patent pi cites a patent pj, then the value of pi decreases. So, differently from classical scientific paper citation scenario, in this one performing a citation has a cost for the citing entity. This fact is not considered by all the approaches conceived to investigate paper citations. Nevertheless, this feature represents the core of patent citation scenario. The approach has been explicitly conceived to capture this feature. [ABSTRACT FROM AUTHOR]