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To efficiently manage plant diseases, Agriculture Cyber-Physical Systems (A-CPS) have been developed to detect and localize disease infestations by integrating the Internet of Agro-Things (IoAT). By the nature of plant and pathogen interactions, the spread of a disease appears as a focus with density of infected plants and intensity of infection diminishing outwards. This gradient of infection needs variable rate and precision pesticide spraying to efficiently utilize resources and effectively handle the diseases. This article, SprayCraft presents a graph based method for disease management A-CPS to identify disease hotspots and compute near optimal path for a spraying drone to perform variable rate precision spraying. It uses graph to represent the diseased locations and their spatial relation, Message Passing is performed over the graph to compute the probability of a location to be a disease hotspot. These probabilities also serve as disease intensity measures and are used for variable rate spraying at each location. Whereas, the graph is utilized to compute tour path by considering it as Traveling Salesman Problem (TSP) for precision spraying by the drone. Proposed method has been validated on synthetic data of locations of diseased locations in a farmland., Comment: 28 pages, 40 figures, 2 tables

Many mobile networks are represented as graphs to obtain insight to their connectivity and transmission properties. Among these properties centrality resilience, that is, how well centralities, such as closeness and betweennesss, are maintained under attacks is a critical factor for proper functioning of a network. In this paper, we study the centrality resilience of complex networks by developing attack models to disrupt the rank of the top path-based centrality vertices. To develop our attack models, we extend the concept of rich clubs of influential vertices to the more general framework of scattered rich clubs. We define scattered rich clubs as dense subgraphs of high centrality vertices that are spread (scattered) across the network. Finding scattered rich clubs, although of polynomial time complexity, is extremely expensive computationally. We use snowball sampling to identify these important substructures as well as to identify which edges to target in our proposed attack models. Our results over a set of real world networks demonstrate that our proposed algorithm is effective in finding the single or scattered rich clubs efficiently and in successfully disrupting the centrality rankings of the network. To summarize, we propose sampling-based attack models for testing the resilience of networks with respect to centrality rankings. As part of this process, we introduce scattered rich clubs, a generalized form of the rich club model, efficient algorithms to detect them, and demonstrate their relation to network resilience., Comment: 10 pages, 8 figures, 3 tables

Any large complex data analysis to infer or discover meaningful information/knowledge involves the following steps (in addition to data collection, cleaning, preparing the data for analysis such as attribute elimination): i) Modeling the data -- an approach for modeling and deriving a data representation for analysis using that approach, ii) translating analysis objectives into computations on the model generated; this can be as simple as a single computation (e.g., community detection) or may involve a sequence of operations (e.g., pair-wise community detection over multiple networks) using expressions based on the model, iii) computation of the expressions generated -- efficiency and scalability come into picture here, and iv) drill-down of results to interpret or understand them clearly. Beyond this, it is also meaningful to visualize results for easier understanding. Covid-19 visualization dashboard presented in this paper is an example of this. This paper covers all of the above steps of data analysis life cycle using a data representation that is gaining importance for multi-entity, multi-feature data sets - Multilayer Networks. We use several data sets to establish the effectiveness of modeling using MLNs and analyze them using the proposed decoupling approach. For coverage, we use different types of MLNs for modeling, and community and centrality computations for analysis. The data sets used - US commercial airlines, IMDb, DBLP, and Covid-19 data set. Our experimental analyses using the identified steps validate modeling, breadth of objectives that can be computed, and overall versatility of the life cycle approach. Correctness of results is verified, where possible, using independently available ground truth. We demonstrate drill-down that is afforded by this approach (due to structure and semantics preservation) for a better understanding and visualization of results.

As the use of MultiLayer Networks (or MLNs) for modeling and analysis is gaining popularity, it is becoming increasingly important to propose a community definition that encompasses the multiple features represented by MLNs and develop algorithms for efficiently computing communities on MLNs. Currently, communities for MLNs, are based on aggregating the networks into single graphs using different techniques (type independent, projection-based, etc.) and applying single graph community detection algorithms, such as Louvain and Infomap on these graphs. This process results in different types of information loss (semantics and structure). To the best of our knowledge, in this paper we propose, for the first time, a definition of community for heterogeneous MLNs (or HeMLNs) which preserves semantics as well as the structure. Additionally, our basic definition can be extended to appropriately match the analysis objectives as needed. In this paper, we present a structure and semantics preserving community definition for HeMLNs that is compatible with and is an extension of the traditional definition for single graphs. We also present a framework for its efficient computation using a newly proposed decoupling approach. First, we define a k-community for connected k layers of a HeMLN. Then we propose a family of algorithms for its computation using the concept of bipartite graph pairings. Further, for a broader analysis, we introduce several pairing algorithms and weight metrics for composing binary HeMLN communities using participating community characteristics. Essentially, this results in an extensible family of community computations. We provide extensive experimental results for showcasing the efficiency and analysis flexibility of the proposed computation using popular IMDb and DBLP data sets., Comment: arXiv admin note: substantial text overlap with arXiv:1910.01737, arXiv:1903.02641

Datasets of real-world applications are characterized by entities of different types, which are defined by multiple features and connected via varied types of relationships. A critical challenge for these datasets is developing models and computations to support flexible analysis, i.e., the ability to compute varied types of analysis objectives in an efficient manner. To address this problem, in this paper, we make a case for modeling such complex data sets as multilayer networks (or MLNs), and argue that MLNs provide a more informative model than the currently popular simple and attribute graphs. Through analyzing communities and hubs on homogeneous and heterogeneous MLNs, we demonstrate the flexibility of the chosen model. We also show that compared to current analysis approaches, a network decoupling-based analysis of MLNs is more efficient and also preserves the structure and result semantics. We use three diverse data sets to showcase the effectiveness of modeling them as MLNs and analyzing them using the decoupling-based approach. We use both homogeneous and heterogeneous MLNs for modeling and community and hub computations for analysis. The data sets are from US commercial airlines and IMDb, a large international movie data set. Our experimental analysis validate modeling, efficiency of computation, and versatility of the approach. Correctness of results are verified using independently available ground truth. For the data sets used, efficiency improvement is in the range of 64% to 98%.

Multilayer networks or MLNs (also called multiplexes or network of networks) are being used extensively for modeling and analysis of data sets with multiple entity and feature types and associated relationships. Although the concept of community is widely-used for aggregate analysis, a structure- and semantics preserving definition for it is lacking for MLNs. Retention of original MLN structure and entity relationships is important for detailed drill-down analysis. In addition, efficient computation is also critical for large number of analysis. In this paper, we introduce a structure-preserving community definition for MLNs as well as a framework for its efficient computation using the decoupling approach. The proposed decoupling approach combines communities from individual layers to form a serial k-community for connected k layers in a MLN. We propose a new algorithm for pairing communities across layers and introduce several weight metrics for composing communities from two layers using participating community characteristics. In addition to the definition, our proposed approach has a number of desired characteristics. It: i) leverages extant single graph community detection algorithms, ii) introduces several weight metrics that are customized for the community concept, iii) is a new algorithm for pairing communities using bipartite graphs, and iv) experimentally validates the community computation and its efficiency on widely-used IMDb and DBLP data sets., Comment: arXiv admin note: substantial text overlap with arXiv:1903.02641

Networks (or graphs) are used to model the dyadic relations between entities in a complex system. In cases where there exists multiple relations between the entities, the complex system can be represented as a multilayer network, where the network in each layer represents one particular relation (or feature). The analysis of multilayer networks involves combining edges from specific layers and then computing a network property. Different subsets of the layers can be combined. For any Boolean combination operation (e.g. AND, OR), the number of possible subsets is exponential to the number of layers. Thus recomputing for each subset from scratch is an expensive process. In this paper, we propose to efficiently analyze multilayer networks using a method that we term network decomposition. Network decomposition is based on analyzing each network layer individually and then aggregating the analysis results. We demonstrate the effectiveness of using network decomposition for detecting communities on different combinations of network layers. Our results on multilayer networks obtained from real-world and synthetic datasets show that our proposed network decomposition method requires significantly lower computation time while producing results of high accuracy.

Multilayer networks or MLNs (also called multiplexes or network of networks) are being used extensively for modeling and analysis of data sets with multiple entity and feature types as well as their relationships. As the concept of communities and hubs are used for these analysis, a structure-preserving definition for them on MLNs (that retains the original MLN structure and node/edge labels and types) and its efficient detection are critical. There is no structure-preserving definition of a community for a MLN as most of the current analyses aggregate a MLN to a single graph. Although there is consensus on community definition for single graphs (and detection packages) and to a lesser extent for homogeneous MLNs, it is lacking for heterogeneous MLNs. In this paper, we not only provide a structure-preserving definition for the first time, but also its efficient computation using a decoupling approach, and discuss its characteristics & significance for analysis. The proposed decoupling approach for efficiency combines communities from individual layers to form a serial k-community for connected k layers in a MLN. We propose several weight metrics for composing layer-wise communities using the bipartite graph match approach based on the analysis semantics. Our proposed approach has a number of advantages. It: i) leverages extant single graph community detection algorithms, ii) is based on the widely-used maximal flow bipartite graph matching for composing k layers, iii) introduces several weight metrics that are customized for the community concept, and iv) experimentally validates the definition, mapping, and efficiency from a flexible analysis perspective on widely-used IMDb data set. Keywords: Heterogeneous Multilayer Networks; Bipartite Graphs; Community Definition and Detection; Decoupling-Based Composition, Comment: 27 pages, Submitted to VLDB 2019

Many scale-free networks exhibit a rich club structure, where high degree vertices form tightly interconnected subgraphs. In this paper, we explore the emergence of rich clubs in the context of shortest path based centrality metrics. We term these subgraphs of connected high closeness or high betweeness vertices as rich centrality clubs (RCC). Our experiments on real world and synthetic networks highlight the inter-relations between RCCs, expander graphs, and the core-periphery structure of the network. We show empirically and theoretically that RCCs exist, if the core-periphery structure of the network is such that each shell is an expander graph, and their density decreases from inner to outer shells. The main contributions of our paper are: (i) we demonstrate that the formation of RCC is related to the core-periphery structure and particularly the expander like properties of each shell, (ii) we show that the RCC property can be used to find effective seed nodes for spreading information and for improving the resilience of the network under perturbation and, finally, (iii) we present a modification algorithm that can insert RCC within networks, while not affecting their other structural properties. Taken together, these contributions present one of the first comprehensive studies of the properties and applications of rich clubs for path based centralities., Comment: Accepted at ACM CIKM 2018, 10 Pages

Vertices with high betweenness and closeness centrality represent influential entities in a network. An important problem for time varying networks is to know a-priori, using minimal computation, whether the influential vertices of the current time step will retain their high centrality, in the future time steps, as the network evolves. In this paper, based on empirical evidences from several large real world time varying networks, we discover a certain class of networks where the highly central vertices are part of the innermost core of the network and this property is maintained over time. As a key contribution of this work, we propose novel heuristics to identify these networks in an optimal fashion and also develop a two-step algorithm for predicting high centrality vertices. Consequently, we show for the first time that for such networks, expensive shortest path computations in each time step as the network changes can be completely avoided; instead we can use time series models (e.g., ARIMA as used here) to predict the overlap between the high centrality vertices in the current time step to the ones in the future time steps. Moreover, once the new network is available in time, we can find the high centrality vertices in the top core simply based on their high degree., Comment: Accepted in Journal Track of ECML PKDD 2018

Holistic analysis of many real-world problems are based on data collected from multiple sources contributing to some aspect of that problem. The word fusion has also been used in the literature for such problems involving disparate data types. Holistically understanding traffic patterns, causes of accidents, bombings, terrorist planning and many natural phenomenon such as storms, earthquakes fall into this category. Some may have real-time requirements and some may need to be analyzed after the fact (post-mortem or forensic analysis.) What is common for all these problems is that the amount and types of data associated with the event. Data may also be incomplete and trustworthiness of sources may also vary. Currently, manual and ad-hoc approaches are used in aggregating data in different ways for analyzing and understanding these problems. In this paper, we approach this problem in a novel way using multilayered networks. We identify features of a central event and propose a network layer for each feature. This approach allows us to study the effect of each feature independently and its impact on the event. We also establish that the proposed approach allows us to compose these features in arbitrary ways (without loss of information) to analyze their combined effect. Additionally, formulation of relationships (e.g., distance measure for a single feature instead of several at the same time) is simpler. Further, computations can be done once on each layer in this approach and reused for mixing and matching the features for aggregate impacts and "what if" scenarios to understand the problem holistically. This has been demonstrated by recreating the communities for the AND-Composed network by using the communities of the individual layers. We believe that techniques proposed here make an important contribution to the nascent yet fast growing area of data fusion.

Networks created from real-world data contain some inaccuracies or noise, manifested as small changes in the network structure. An important question is whether these small changes can significantly affect the analysis results. In this paper, we study the effect of noise in changing ranks of the high centrality vertices. We compare, using the Jaccard Index (JI), how many of the top-k high centrality nodes from the original network are also part of the top-k ranked nodes from the noisy network. We deem a network as stable if the JI value is high. We observe two features that affect the stability. First, the stability is dependent on the number of top-ranked vertices considered. When the vertices are ordered according to their centrality values, they group into clusters. Perturbations to the network can change the relative ranking within the cluster, but vertices rarely move from one cluster to another. Second, the stability is dependent on the local connections of the high ranking vertices. The network is highly stable if the high ranking vertices are connected to each other. Our findings show that the stability of a network is affected by the local properties of high centrality vertices, rather than the global properties of the entire network. Based on these local properties we can identify the stability of a network, without explicitly applying a noise model., Comment: CIKM 2016

Network analysis is an important tool in understanding the behavior of complex systems of interacting entities. However, due to the limitations of data gathering technologies, some interactions might be missing from the network model. This is a ubiquitous problem in all domains that use network analysis, from social networks to hyper-linked web networks to biological networks. Consequently, an important question in analyzing networks is to understand how increasing the noise level (i.e. percentage of missing edges) affects different network parameters. In this paper we evaluate the effect of noise on community scoring and centrality-based parameters with respect to two different aspects of network analysis: (i) sensitivity, that is how the parameter value changes as edges are removed and (ii) reliability in the context of message spreading, that is how the time taken to broadcast a message changes as edges are removed. Our experiments on synthetic and real-world networks and three different noise models demonstrate that for both the aspects over all networks and all noise models, permanence qualifies as the most effective metric. For the sensitivity experiments closeness centrality is a close second. For the message spreading experiments, closeness and betweenness centrality based initiator selection closely competes with permanence. This is because permanence has a dual characteristic where the cumulative permanence over all vertices is sensitive to noise but the ids of the top-rank vertices, which are used to find seeds during message spreading remain relatively stable under noise., Comment: Accepted in proceedings of ASONAM 2016

The goal of community detection algorithms is to identify densely-connected units within large networks. An implicit assumption is that all the constituent nodes belong equally to their associated community. However, some nodes are more important in the community than others. To date, efforts have been primarily driven to identify communities as a whole, rather than understanding to what extent an individual node belongs to its community. Therefore, most metrics for evaluating communities, for example modularity, are global. These metrics produce a score for each community, not for each individual node. In this paper, we argue that the belongingness of nodes in a community is not uniform. The central idea of permanence is based on the observation that the strength of membership of a vertex to a community depends upon two factors: (i) the the extent of connections of the vertex within its community versus outside its community, and (ii) how tightly the vertex is connected internally. We discuss how permanence can help us understand and utilize the structure and evolution of communities by demonstrating that it can be used to -- (i) measure the persistence of a vertex in a community, (ii) design strategies to strengthen the community structure, (iii) explore the core-periphery structure within a community, and (iv) select suitable initiators for message spreading. We demonstrate that the process of maximizing permanence produces meaningful communities that concur with the ground-truth community structure of the networks more accurately than eight other popular community detection algorithms. Finally, we show that the communities obtained by this method are (i) less affected by the changes in vertex-ordering, and (ii) more resilient to resolution limit, degeneracy of solutions and asymptotic growth of values., Comment: 34 pages, 15 figures, 8 tables, ACM Transactions on Knowledge Discovery from Data (TKDD), 2016. arXiv admin note: text overlap with arXiv:1206.4987 by other authors

Detection of non-overlapping and overlapping communities are essentially the same problem. However, current algorithms focus either on finding overlapping or non-overlapping communities. We present a generalized framework that can identify both non-overlapping and overlapping communities, without any prior input about the network or its community distribution. To do so, we introduce a vertex-based metric, GenPerm, that quantifies by how much a vertex belongs to each of its constituent communities. Our community detection algorithm is based on maximizing the GenPerm over all the vertices in the network. We demonstrate, through experiments over synthetic and real-world networks, that GenPerm is more effective than other metrics in evaluating community structure. Further, we show that due to its vertex-centric property, GenPerm can be used to unfold several inferences beyond community detection, such as core-periphery analysis and message spreading. Our algorithm for maximizing GenPerm outperforms six state-of-the-art algorithms in accurately predicting the ground-truth labels. Finally, we discuss the problem of resolution limit in overlapping communities and demonstrate that maximizing GenPerm can mitigate this problem., Comment: This paper (final version) is accepted in IEEE Transactions on Knowledge and Data Engineering (TKDE). 13 Figures, 6 tables

Despite the prevalence of community detection algorithms, relatively less work has been done on understanding whether a network is indeed modular and how resilient the community structure is under perturbations. To address this issue, we propose a new vertex-based metric called "permanence", that can quantitatively give an estimate of the community-like structure of the network. The central idea of permanence is based on the observation that the strength of membership of a vertex to a community depends upon the following two factors: (i) the distribution of external connectivity of the vertex to individual communities and not the total external connectivity, and (ii) the strength of its internal connectivity and not just the total internal edges. In this paper, we demonstrate that compared to other metrics, permanence provides (i) a more accurate estimate of a derived community structure to the ground-truth community and (ii) is more sensitive to perturbations in the network. As a by-product of this study, we have also developed a community detection algorithm based on maximizing permanence. For a modular network structure, the results of our algorithm match well with ground-truth communities., Comment: 10 pages, 5 figures, 8 tables, Accepted in 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining

Identifying community structure is a fundamental problem in network analysis. Most community detection algorithms are based on optimizing a combinatorial parameter, for example modularity. This optimization is generally NP-hard, thus merely changing the vertex order can alter their assignments to the community. However, there has been very less study on how vertex ordering influences the results of the community detection algorithms. Here we identify and study the properties of invariant groups of vertices (constant communities) whose assignment to communities are, quite remarkably, not affected by vertex ordering. The percentage of constant communities can vary across different applications and based on empirical results we propose metrics to evaluate these communities. Using constant communities as a pre-processing step, one can significantly reduce the variation of the results. Finally, we present a case study on phoneme network and illustrate that constant communities, quite strikingly, form the core functional units of the larger communities., Comment: 31 pages, 9 figures