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We investigate how bots influence human-to-human interaction in online communities. In doing so, we distinguish between reflexive and supervisory bots delegated by community participants and moderators, respectively. We hypothesize that reflexive bot activity will reduce direct reciprocity and increase generalized reciprocity and that supervisory bot activity will reduce preferential attachment among human participants. Through an analysis of almost 70 million posts on the discussion communities on Reddit, a popular platform for online discussions, we found support for the hypotheses. [ABSTRACT FROM AUTHOR]

We study the evolution of the friendship index in complex social networks over time. The elements of the networks are the users, and the connections correspond to the interactions between them. The friendship index of a node is defined as the ratio of the average degree of its neighbors to the degree of the node itself. Obviously, in the process of network growth, the value of the friendship index for any node in the network may change due to the fact that new edges can be attached to this node or its neighbors. In this paper, we study the dynamics of the friendship index of a single node over time for growth networks generated on the basis of the preferential attachment mechanism. We find both the asymptotics of their expected values and the variances over time. In addition, we analyze the behavior of the friendship index for five real networks. [ABSTRACT FROM AUTHOR]

We explore a simple model of network dynamics which has previously been applied to the study of information flow in the context of epidemic spreading. A random rooted network is constructed that evolves according to the following rule: at a constant rate, pairs of nodes (i , j) are randomly chosen to interact, with an edge drawn from i to j (and any other out-edge from i deleted) if j is strictly closer to the root with respect to graph distance. We characterise the dynamics of this random network in the limit of large size, showing that it instantaneously forms a tree with long branches that immediately collapse to depth two, then it slowly rearranges itself to a star-like configuration. This curious behaviour has consequences for the study of the epidemic models in which this information network was first proposed. [ABSTRACT FROM AUTHOR]

We study the evolution of the friendship index in complex social networks over time. The elements of the networks are the users, and the connections correspond to the interactions between them. The friendship index of a node is defined as the ratio of the average degree of its neighbors to the degree of the node itself. Obviously, in the process of network growth, the value of the friendship index for any node in the network may change due to the fact that new edges can be attached to this node or its neighbors. In this paper, we study the dynamics of the friendship index of a single node over time for growth networks generated on the basis of the preferential attachment mechanism. We find both the asymptotics of their expected values and the variances over time. In addition, we analyze the behavior of the friendship index for five real networks.

A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index is a measure of clustering (or local dependence) of the stochastic process. The cluster implies a set of consecutive exceedances of the process over a sufficiently high threshold. Our recent results concerning sums and maxima of non-stationary random length sequences of regularly varying random variables are extended to random graphs. Starting with a set of connected stationary seed communities as a hot spot and ranking them with regard to their tail indices, the tail and extremal indices of new nodes that are appended to the network may be determined. This procedure allows us to predict a temporal network evolution in terms of tail and extremal indices. The extremal index determines limiting distributions of a maximum of the PageRank and the Max-Linear Model of newly attached nodes. The exposition is provided by algorithms and examples. To validate our theoretical results, our simulation and real data study concerning a linear preferential attachment as a tool for network growth are provided. [ABSTRACT FROM AUTHOR]

We propose an extension of the preferential attachment scheme by allowing the connecting probability to depend on time t. We estimate the parameters involved in the model by minimizing the expected squared difference between the number of vertices of degree one and its conditional expectation. The asymptotic properties of the estimators are also investigated when the parameters are time-varying by establishing the central limit theorem (CLT) of the number of vertices of degree one. We propose a new statistic to test whether the parameters have change points. We also offer some methods to estimate the number of change points and detect the locations of change points. Simulations are conducted to illustrate the performances of the above results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability 1 - f (t) . We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation - γ , where γ ∈ [ 0 , 1) . We also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient. [ABSTRACT FROM AUTHOR]

Phonological networks are representations of word forms and their phonological relationships with other words in a given language lexicon. A principle underlying the growth (or evolution) of those networks is preferential attachment, or the "rich-gets-richer" mechanisms, according to which words with many phonological neighbors (or links) are the main beneficiaries of future growth opportunities. Due to their limited number of words, language lexica constitute node-constrained networks where growth cannot keep increasing in a linear way; hence, preferential attachment is likely mitigated by certain factors. The present study investigated obsolescence effects (i.e., a word's finite timespan of being active in terms of growth) in an evolving phonological network of English as a second language. It was found that phonological neighborhoods are constructed by one large initial lexical spurt, followed by sublinear growth spurts that eventually lead to very limited growth in later lexical spurts during network evolution. First-language-given neighborhood densities are rarely reached even by the most advanced language learners. An analysis of the strength of phonological relationships between phonological word forms revealed a tendency to incorporate phonetically more distant phonological neighbors at earlier acquisition stages. Overall, the findings suggest an obsolescence effect in growth that favors younger words. Implications for the second-language lexicon include leveraged learning mechanisms and learning bouts focused on a smaller range of phonological segments, and involve questions concerning lexical processing in aging networks. [ABSTRACT FROM AUTHOR]

It is recognized that most real systems and networks exhibit a much higher clustering with comparison to a random null model, which can be explained by a higher probability of the triad formation—a pair of nodes with a mutual neighbor have a greater possibility of having a link between them. To catch the more substantial clustering of real-world networks, the model based on the triadic closure mechanism was introduced by P. Holme and B. J. Kim in 2002. It includes a "triad formation step" in which a newly added node links both to a preferentially chosen node and to its randomly chosen neighbor, therefore forming a triad. In this study, we propose a new model of network evolution in which the triad formation mechanism is essentially changed in comparison to the model of P. Holme and B. J. Kim. In our proposed model, the second node is also chosen preferentially, i.e., the probability of its selection is proportional to its degree with respect to the sum of the degrees of the neighbors of the first selected node. The main goal of this paper is to study the properties of networks generated by this model. Using both analytical and empirical methods, we show that the networks are scale-free with power-law degree distributions, but their exponent γ is tunable which is distinguishable from the networks generated by the model of P. Holme and B. J. Kim. Moreover, we show that the degree dynamics of individual nodes are described by a power law. [ABSTRACT FROM AUTHOR]

The mechanisms of network generation have undergone extensive analysis and found broad applications in various real-world scenarios. Among the fruitful literature on network models, numerous studies seek to explore and interpret fundamental graph structure properties, including the clustering effect, exchangeability, and scale-free properties. In this paper, we present a comprehensive review of the statistical modeling methods for the mechanisms of network generation. We specifically focus on three representative classes of models, namely the stochastic block models, the exchangeable network models, and the preferential attachment models. For each model type, our approach begins by reviewing existing methods and model setups, followed by an exploration of the core modeling principles behind them. We also summarize relevant statistical inference techniques and provide a unified understanding of theoretical analyses. Furthermore, we emphasize several challenges and open problems that could shed light on future research. We conclude this review with the identification of some possible directions for future study. [ABSTRACT FROM AUTHOR]

Users of social networks display diversified behavior and online habits. For instance, a user's tendency to reply to a post can depend on the user and the person posting. For convenience, we group users into aggregated behavioral patterns, focusing here on the tendency to reply to or reciprocate messages. The reciprocity feature in social networks reflects the information exchange among users. We study the properties of a preferential attachment model with heterogeneous reciprocity levels, give the growth rate of model edge counts, and prove the convergence of empirical degree frequencies to a limiting distribution. This limiting distribution is not only multivariate regularly varying, but also has the property of hidden regular variation. [ABSTRACT FROM AUTHOR]

Abstract Cross‐affiliation emerges as a new and fast‐developing means to promote collaboration in financial research. We find that the average number of affiliations reported per author in the top‐three finance journals increases steadily from 1.1 to 1.3 from 1995 to 2016. Scale‐free power laws characterize the resulting highly‐skewed distributions of top finance journal publications of worldwide institutions. We propose an explanation of the scale‐invariance, based on a network model featuring nonlinear growth and linear preferential attachment. The model indicates that success‐breeds‐success engenders 87% of total publications and hence the dispersion in research output, while accelerated growth of collaboration reduces the heterogeneity.

This research explores the impacts of regional trade agreements on global trade flows from the perspective of symbiotic evolution. By using network analysis method on 18 years of two-ways (including import and export) of trade flow network matrixes of 136 countries/ regions of the world from 2002 to 2019, the study finds that: 1) Due to the mechanism of the preferential attachment, the global trade pattern obeys the classic law of power distribution, moving from "flat head" to "steep tail" from 2002 to 2019, which results in the clustering phenome‐ non of small world networks. 2) The structure of the global trade network has evolved from the dual pillars led respectively by the U. S. and Germany in 2002 to the tripartite forces of China, the U. S., and Germany. The matching effect drives many peripheral countries and regions to "unite together" and then gradually integrate into the three forces through "preferential attachment", promoting the global trade flow entering a more open world. 3) Intergovernmental trade agreements, as the "visible hand" of governments, can explain 19. 2% of changes in the global trade, which indicates that collaborative cooperation between countries has positive impacts on the evolution of the world trading system. 4) Under the influence of network externalities, multi‐ lateral trade agreements demonstrate greater impetus than bilateral trade agreements to global trade. Countries initiating into the multilateral trade agreements conform not only with the general trend of economic recovery after the epidemic, but it is also beneficial to the bright prospect of a community with a shared future for mankind. [ABSTRACT FROM AUTHOR]

Cross‐affiliation emerges as a new and fast‐developing means to promote collaboration in financial research. We find that the average number of affiliations reported per author in the top‐three finance journals increases steadily from 1.1 to 1.3 from 1995 to 2016. Scale‐free power laws characterize the resulting highly‐skewed distributions of top finance journal publications of worldwide institutions. We propose an explanation of the scale‐invariance, based on a network model featuring nonlinear growth and linear preferential attachment. The model indicates that success‐breeds‐success engenders 87% of total publications and hence the dispersion in research output, while accelerated growth of collaboration reduces the heterogeneity. [ABSTRACT FROM AUTHOR]

Abstract The fundamental objective of the Lightning Network is to establish a decentralized platform for scaling the Bitcoin network and facilitating high-throughput micropayments. However, this network has gradually deviated from its decentralized topology since its operational inception, and its resources have quickly shifted towards centralization. The evolution of the network and the changes in its topology have been critically reviewed and criticized due to its increasing centralization. This study delves into the network’s topology and the reasons behind its centralized evolution. We explain the incentives of various participating nodes in the network and propose a score-based strategy for the Lightning Autopilot system, which is responsible for automatically establishing new payment channels for the nodes joining the network. Our study demonstrates that utilizing the proposed strategy could significantly aid in reducing the network’s centralization. This strategy is grounded in qualitative labeling of network nodes based on topological and protocol features, followed by the creation of a scoring and recommendation model. Results of the experiments indicate that in the evolved network using the proposed strategy, concentration indicators such as the Gini coefficient can decrease by up to 17%, and channels ownership of the top 1% of hubs decrease by 27% compared to other autopilot strategies. Moreover, through simulated targeted attacks on hubs and channels, it is shown that by adopting the proposed strategy, the network’s resilience is increased compared to the existing autopilot strategies for evolved networks. The proposed method from this research can also be integrated into operational Lightning clients and potentially replace the current recommendation methods used in Lightning Autopilot.

Abstract The widely used characterization of scale-free networks as “robust-yet-fragile” originates primarily from experiments on instances generated by preferential attachment. According to this characterization, scale-free networks are more robust against random failures but more fragile against targeted attacks when compared to random networks of the same size. Here, we consider a more appropriate baseline by requiring that the random networks match not only the size but also the inherent minimum degree of preferential-attachment networks they are compared with. Under this more equitable condition, we can (1) prove that random networks are almost surely robust against any vertex removal strategy and (2) show through extensive experiments that scale-free networks generated by preferential attachment are not particularly robust against random failures. Finally, we (3) add experiments demonstrating that preferentially attaching to well-connected vertices does not enhance robustness at all.

Reciprocity in social networks is a measure of information exchange between two individuals, and indicates interaction patterns between pairs of users. A recent study finds that the reciprocity coefficient of a classical directed preferential attachment (PA) model does not match empirical evidence. Towards remedying this deficiency, we extend the classical three-scenario directed PA model by adding a parameter that controls the probability of creating a reciprocal edge. This proposed model also allows edge creation between two existing nodes, making it a realistic candidate for fitting to datasets. We provide and compare two estimation procedures for fitting the new reciprocity model and demonstrate the methods on simulated and real datasets. One estimation method requires careful analysis of the heavy tail properties of the model. The fitted models provide a good match with the empirical tail distributions of both in- and out-degrees but other mismatched diagnostics suggest that further generalization of the model is warranted. [ABSTRACT FROM AUTHOR]

We consider random two‐colorings of random linear preferential attachment trees, which includes recursive trees, plane‐oriented recursive trees, binary search trees, and a class of d‐ary trees. The random coloring is defined by assigning the root the color red or blue with equal probability, and all other vertices are assigned the color of their parent with probability p$$ p $$ and the other color otherwise. These colorings have been previously studied in other contexts, including Ising models and broadcasting, and can be considered as generalizations of bond percolation. With the help of Pólya urns, we prove limiting distributions, after proper rescalings, for the number of vertices, monochromatic subtrees, and leaves of each color, as well as the number of fringe subtrees with two‐colorings. Using methods from analytic combinatorics, we also provide precise descriptions of the limiting distribution after proper rescaling of the size of the root cluster; the largest monochromatic subtree containing the root. [ABSTRACT FROM AUTHOR]

Network robustness in wireless sensor network (WSN) is an emerging area of research as sensor nodes (SNs) often fail due to limited energy resources, harsh environment, and proliferation of cyber-attacks. Therefore, the energy efficiency and robustness of SNs are the two critical issues that need to be addressed in WSNs. In this paper, we address the above mentioned issues in two phases. In the first phase, we propose an energy efficient SN deployment scheme for WSNs using non-uniform SN deployment scheme. In the second phase, we generate scale-free network topology in order to improve the robustness of WSN so that they can withstand failure issues due to cyber-attacks. For the construction of scale-free topology, we have considered various constraints of SNs viz., communication range, maximum degree, and network growth. This topology construction was proved to be very effective in providing robustness to WSN because of their heterogeneous degree distribution. The performance of the proposed work has been evaluated through simulation using Python 3.7.1 on Spyder 3.3.2 on Ubuntu 19.10 with Linux Kernel 5.0.0.13-generic, X86_64 operating system. The simulation results show that the proposed work significantly outperforms existing state-of-the-art related approaches in terms of robustness of the WSN along with the increase in network lifetime. Also, it produces characteristic at tailed distribution with maximum SNs having fewer degree count. [ABSTRACT FROM AUTHOR]

We study potential biases of popular network clustering quality metrics, such as those based on the dichotomy between internal and external connectivity. We propose a method that uses both stochastic and preferential attachment block models construction to generate networks with preset community structures, and Poisson or scale-free degree distribution, to which quality metrics will be applied. These models also allow us to generate multi-level structures of varying strength, which will show if metrics favour partitions into a larger or smaller number of clusters. Additionally, we propose another quality metric, the density ratio. We observed that most of the studied metrics tend to favour partitions into a smaller number of big clusters, even when their relative internal and external connectivity are the same. The metrics found to be less biased are modularity and density ratio. [ABSTRACT FROM AUTHOR]

Citation score has become a very important metric to assess the quality of a publication in the current global ranking scenario. In this context, the study of citation networks gains importance as it helps in understanding the citation process as well as in analyzing citation trends in the research world. Citation networks are modeled as directed acyclic graphs in which publications of the authors are considered as nodes and citations between the papers form the links. In this paper, we propose an additive Time-Stamp based Network Evolution(TNE) model for citation networks, extending Price's preferential attachment model by including the recency effect on the citation process without neglecting the impact of classical papers. We propose a more meaningful definition of clustering coefficient for citation networks in terms of 'citation triangles'. Further, the network simulated by the TNE model with best-fit parameters is compared with the real-world(DBLP) citation network. The results of various significance tests show that the simulated network matches very well with the DBLP citation network in terms of several network properties. [ABSTRACT FROM AUTHOR]

Jumlah penelitian yang menganalisa data semakin meningkat. Salah satu topik yang populer adalah mencari interaksi antara masing-masing data yang biasa disebut sebagai social network atau jejaring sosial. Metode yang biasa digunakan untuk pemodelan dari masing-masing data adalah link prediction. Dengan menggunakan link prediction akan mendapatkan hasil berupa nilai kesamaan atau hubungan antara masing-masing data. Pemilihan umum Indonesia adalah pesta demokrasi rakyat yang diadakan setiap 5 tahun sekali. Salah satu data yang bisa diambil dalam pemilihan umum adalah data calon legislatif. Penelitian ini mencoba mengimplementasikan link prediction ke dalam data calon legislatif pemilihan umum Indonesia 2019. Peneliti menggunakan teknik crawling untuk mendapatkan sumber data dari website resmi Komisi Pemilihan Umum. Setelah proses crawling data akan dibersihkan sesuai atribut terpilih. Atribut yang digunakan untuk mencari nilai kesamaan adalah daerah asal, daerah pemilihan, dan partai pengusung. Metode link prediction yang digunakan adalah Adamic-Adar Index, Jaccard Coefficient, dan Preferential Attachment. Hasil penelitian ini menemukan bahwa jumlah kesamaan berdasarkan atribut terpilhi masing-masing calon legislatif cukup besar.

Our objective is to survey recent results concerning the evolution of random networks and related extreme value statistics, which are a subject of interest due to numerous applications. Our survey concerns the statistical methodology but not the structure of random networks. We focus on the problems arising in evolving networks mainly due to the heavy-tailed nature of node indices. Tail and extremal indices of the node influence characteristics like in-degrees, out-degrees, PageRanks, and Max-linear models arising in the evolving random networks are discussed. Related topics like preferential and clustering attachments, community detection, stationarity and dependence of graphs, information spreading, finding the most influential leading nodes and communities, and related methods are surveyed. This survey tries to propose possible solutions to unsolved problems, like testing the stationarity and dependence of random graphs using known results obtained for random sequences. We provide a discussion of unsolved or insufficiently developed problems like the distribution of triangle and circle counts in evolving networks, or the clustering attachment and the local dependence of the modularity, the impact of node or edge deletion at each step of evolution on extreme value statistics, among many others. Considering existing techniques of community detection, we pay attention to such related topics as coloring graphs and anomaly detection by machine learning algorithms based on extreme value theory. In order to understand how one can compute tail and extremal indices on random graphs, we provide a structured and comprehensive review of their estimators obtained for random sequences. Methods to calculate the PageRank and PageRank vector are shortly presented. This survey aims to provide a better understanding of the directions in which the study of random networks has been done and how extreme value analysis developed for random sequences can be applied to random networks. [ABSTRACT FROM AUTHOR]

The aim of this study was to study the underlying structural characteristics of networks formed by debtor-creditor relationships. According to attributes of P2P lending, this paper model the networks of debtor-creditor relationships as an evolving network with the addition and deletion of nodes. It was found that networks of debtor-creditor relationships are scale-free networks. When the impact of default was considered in networks of debtor-creditor relationships, it was found that the power-law distribution of degree is not changed by the event of default, but the exponent of power-law under the event of default is less than the situation without the event of default. Our results enrich the application of complex networks. [ABSTRACT FROM AUTHOR]

We construct a model of cyclical growth with agent-based features designed to study the network origins of aggregate fluctuations from a demand-side perspective. In our model, aggregate fluctuations result from variations in investment behaviour at firm level motivated by endogenously-generated changes in 'animal spirits'. In addition to being influenced by their own economic conditions, firms pay attention to the performance of first-degree network neighbours, weighted (to differing degrees) by the centrality of these neighbours in the network, when revising their animal spirits. This allows us to analyse the effects of the centrality of linked network neighbours on the amplitude of aggregate fluctuations. We show that the amplitude of fluctuations is significantly affected by the eigenvector centrality, and the weight attached to the eigenvector centrality, of linked network neighbours. The dispersion of this effect about its mean is shown to be similarly important, resulting in the possibility that network properties can result in 'great moderations' giving way to sudden increases in the volatility of aggregate economic performance. • Studies 'granular' origins of aggregate fluctuations in a demand-led economy. • Firms' revision of animal spirits influenced by linked network neighbours. • Firms pay attention to linked network neighbours in accordance with their centrality. • Eigenvector centrality significantly affects the amplitude of aggregate fluctuations. • Dispersion of this effect might explain the onset and demise of 'great moderations'. [ABSTRACT FROM AUTHOR]

In this paper, we propose a class of random trees, the evolution of which is an integration of uniform and preferential attachments. Hence, they are called hybrid recursive trees (HRTs). The goal of this paper is to characterize the structure of HRTs. At first, we investigate the degree profile of HRTs by determining the exact and asymptotic mean of the degree of a node with fixed label. Next, we show that the limit distribution of the number of leaves of HRTs is Gaussian, and that the degree distribution follows a power law, suggesting that HRTs are scale-free. At last, we look into the Zagreb index of HRTs, where the first two moments are calculated. [ABSTRACT FROM AUTHOR]

We study potential biases of popular network clustering quality metrics, such as those based on the dichotomy between internal and external connectivity. We propose a method that uses both stochastic and preferential attachment block models construction to generate networks with preset community structures, and Poisson or scale-free degree distribution, to which quality metrics will be applied. These models also allow us to generate multi-level structures of varying strength, which will show if metrics favour partitions into a larger or smaller number of clusters. Additionally, we propose another quality metric, the density ratio. We observed that most of the studied metrics tend to favour partitions into a smaller number of big clusters, even when their relative internal and external connectivity are the same. The metrics found to be less biased are modularity and density ratio.

Private businesses are often entrusted with public contracts, wherein public money is allocated to a private company. This process raises concerns about transparency, even in the most developed democracies. But are there any regularities guiding this process? Do all private companies benefit equally from the state budgets? Here, we tackle these questions focusing on the case of Slovenia, which keeps excellent records of this kind of public spending. We examine a dataset detailing every transfer of public money to the private sector from January 2003 to May 2020. During this time, Slovenia has conducted business with no less than 248 989 private companies. We find that the cumulative distribution of money received per company can be reasonably well explained by a power-law or lognormal fit. We also show evidence for the first-mover advantage, and determine that companies receive new funding in a way that is roughly linear over time. These results indicate that, despite all human factors involved, Slovenian public spending is at least to some extent regulated by emergent self-organizing principles.

It is recognized that most real systems and networks exhibit a much higher clustering with comparison to a random null model, which can be explained by a higher probability of the triad formation—a pair of nodes with a mutual neighbor have a greater possibility of having a link between them. To catch the more substantial clustering of real-world networks, the model based on the triadic closure mechanism was introduced by P. Holme and B. J. Kim in 2002. It includes a “triad formation step” in which a newly added node links both to a preferentially chosen node and to its randomly chosen neighbor, therefore forming a triad. In this study, we propose a new model of network evolution in which the triad formation mechanism is essentially changed in comparison to the model of P. Holme and B. J. Kim. In our proposed model, the second node is also chosen preferentially, i.e., the probability of its selection is proportional to its degree with respect to the sum of the degrees of the neighbors of the first selected node. The main goal of this paper is to study the properties of networks generated by this model. Using both analytical and empirical methods, we show that the networks are scale-free with power-law degree distributions, but their exponent γ is tunable which is distinguishable from the networks generated by the model of P. Holme and B. J. Kim. Moreover, we show that the degree dynamics of individual nodes are described by a power law.

Preferential attachment (PA) is a widely observed behavior in many living systems and has been used in modeling many networks. The aim of this work is to show that the mechanism of PA is a consequence of the fundamental principle of least effort. We derive PA directly from this principle in maximizing an efficiency function. This approach not only allows a better understanding of the different PA mechanisms already reported but also naturally extends these mechanisms with a non-power law probability of attachment. The possibility of using the efficiency function as a general measure of attachment efficiency is also investigated. [ABSTRACT FROM AUTHOR]

The degree distributions of complex networks are usually considered to follow a power law distribution. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-world network. The main idea is to invert the recurrence equation commonly used to compute the degree distribution in order to find a convenient attachment function for node connections - commonly chosen as linear. We compute this attachment function for some classical distributions, as the power-law, the broken power-law, and the geometric distributions. We also use the model on an undirected version of the Twitter network, for which the degree distribution has an unusual shape. We finally show that the divergence of chosen attachment functions is directly linked to the heavy-tailed property of the obtained degree distributions. [ABSTRACT FROM AUTHOR]

Many classic networks grow by hooking small components via vertices. We introduce a class of networks that grows by fusing the edges of a small graph to an edge chosen uniformly at random from the network. For this random edge-hooking network, we study the local degree profile, that is, the evolution of the average degree of a vertex over time. For a special subclass, we further determine the exact distribution and an asymptotic gamma-type distribution. We also study the "core," which consists of the well-anchored edges that experience fusing. A central limit theorem emerges for the size of the core. At the end, we look at an alternative model of randomness attained by preferential hooking, favoring edges that experience more fusing. Under preferential hooking, the core still follows a Gaussian law but with different parameters. Throughout, Pólya urns are systematically used as a method of proof. [ABSTRACT FROM AUTHOR]

Numerous works have been proposed to generate random graphs preserving the same properties as real-life large-scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs exist, and also, just a few models allow to both preserve a power-law degree distribution and a high modularity indicating the presence of communities. We present a dynamic preferential attachment hypergraph model which features partition into communities. We prove that its degree distribution follows a power-law, and we give theoretical lower bounds for its modularity. We compare its characteristics with a real-life co-authorship network and show that our model achieves good performances. We believe that our hypergraph model will be an interesting tool that may be used in many research domains in order to reflect better real-life phenomena. [ABSTRACT FROM AUTHOR]

We consider the duration of discussions in face-to-face contacts and propose a stochastic model to describe it. It is based on the points of a Levy flight where the duration of each contact corresponds to the size of the clusters produced during the walk. When confronting it to the data measured from proximity sensors, we show that several datasets obtained in different environments, are precisely reproduced by the model fixing a single parameter, the Levy index, to 1.15. We analyze the dynamics of the cluster formation during the walk and compute analytically the cluster size distribution. We find that discussions are first driven by a maximum-entropy geometric distribution and then by a rich-get-richer mechanism reminiscent of preferential-attachment (the more a discussion lasts, the more it is likely to continue). In this model, conversations may be viewed as an aggregation process with a characteristic scale fixed by the mean interaction time between the two individuals. • First-time model for describing the dynamics of a face-to-face relation. • Contact duration is related to the size of clusters in a Levy walk. • A Levy index of 1.15 matches precisely several datasets (incl. baboons). • Analytical computation of the cluster size distribution in Levy walks. • Dynamics of cluster formation is similar to the way discussions evolve. [ABSTRACT FROM AUTHOR]

Tree-based systems rely on real-time dissemination trees to deliver information to nodes. In order to offer good services, two fundamental aspects should guide the real-time growth process: low node degree and short distances to the server. In this paper, we propose a growth process to construct trees and make a detailed study on modeling and performance analysis of these tree-based systems. Our generative mechanism is based on the preferential attachment principle, where preference is given in terms of node quality. The proposed growth mechanism has a single parameter to weigh the relative importance of node degree and node distance on assessing node quality. We aim at understanding this mechanism when considering the local aspect of the node’s degree and the global aspect of the distance to a source. With this goal, we investigate our model through simulations and compare it to other growth processes. Our results indicate that the proposed model is capable of self-organizing nodes into good trees under six metrics of interest.

Temporal datasets that describe complex interactions between individuals over time are increasingly common in various domains. Conventional graph representations of such datasets may lead to information loss since higher-order relationships between more than two individuals must be broken into multiple pairwise relationships in graph representations. In those cases, a hypergraph representation is preferable since it can preserve higher-order relationships by using hyperedges. However, existing hypergraph models of temporal complex networks often employ some data-independent growth mechanism, which is the linear preferential attachment in most cases. In principle, this pre-specification is undesirable since it completely ignores the data at hand. Our work proposes a new hypergraph growth model with a data-driven preferential attachment mechanism estimated from observed data. A key component of our method is a recursive formula that allows us to overcome a bottleneck in computing the normalizing factors in our model. We also treat an often-neglected selection bias in modeling the emergence of new edges with new nodes. Fitting the proposed hypergraph model to 13 real-world datasets from diverse domains, we found that all estimated preferential attachment functions deviates substantially from the linear form. This demonstrates the need of doing away with the linear preferential attachment assumption and adopting a data-driven approach. We also showed that our model outperformed conventional models in replicating the observed first-order and second-order structures in these real-world datasets.