Testing-Based Community Detection Methods for Complex Networks

Community detection is an exploratory method of grouping strongly connected nodes in a network, in most cases using only the network edge structure as a guide. Using discovered communities for downstream analyses can be crucial for real-world decision-making and inference. Recent approaches to community detection include testing-based community extraction, a process in which communities are refined one-by-one via analysis of graph statistics. However, to date, testing-based extraction methods are tied to the configuration model as a null, which applies only to single-layer, binary graphs. In this thesis, testing-based extraction is generalized to arbitrary networks types with a framework called Node-Set Testing (NST). The NST framework defines the broader statistical elements of an approach that uses hypothesis testing to detect communities in complex networks. The NST framework is applied to (i) weighted networks and (ii) bipartite correlation networks, resulting in novel community detection algorithms. In particular, new null models and test statistics are specified to apply iterative hypothesis-testing algorithms on these types of networks. Detailed analyses of the empirical and theoretical properties of the proposed methods are provided. Other chapters in this thesis, while not explicitly involving testing-based algorithms, support the discussion of community detection in heterogeneous networks. One chapter provides a consistency analysis of a significance-based score for community extraction in multilayer networks. In another chapter, preceding the discussion of the NST method for bipartite correlation networks, an application area called eQTL analysis is discussed. In particular, a new model for estimating the effect size and regression correlation of the links in an eQTL network is introduced and studied.Doctor of Philosoph

Evolution of Network Architecture in a Granular Material Under Compression

As a granular material is compressed, the particles and forces within the system arrange to form complex and heterogeneous collective structures. Force chains are a prime example of such structures, and are thought to constrain bulk properties such as mechanical stability and acoustic transmission. However, capturing and characterizing the evolving nature of the intrinsic inhomogeneity and mesoscale architecture of granular systems can be challenging. A growing body of work has shown that graph theoretic approaches may provide a useful foundation for tackling these problems. Here, we extend the current approaches by utilizing multilayer networks as a framework for directly quantifying the progression of mesoscale architecture in a compressed granular system. We examine a quasi-two-dimensional aggregate of photoelastic disks, subject to biaxial compressions through a series of small, quasistatic steps. Treating particles as network nodes and interparticle forces as network edges, we construct a multilayer network for the system by linking together the series of static force networks that exist at each strain step. We then extract the inherent mesoscale structure from the system by using a generalization of community detection methods to multilayer networks, and we define quantitative measures to characterize the changes in this structure throughout the compression process. We separately consider the network of normal and tangential forces, and find that they display a different progression throughout compression. To test the sensitivity of the network model to particle properties, we examine whether the method can distinguish a subsystem of low-friction particles within a bath of higher-friction particles. We find that this can be achieved by considering the network of tangential forces, and that the community structure is better able to separate the subsystem than a purely local measure of interparticle forces alone. The results discussed throughout this study suggest that these network science techniques may provide a direct way to compare and classify data from systems under different external conditions or with different physical makeup

Multiplex Communities and the Emergence of International Conflict

Advances in community detection reveal new insights into multiplex and multilayer networks. Less work, however, investigates the relationship between these communities and outcomes in social systems. We leverage these advances to shed light on the relationship between the cooperative mesostructure of the international system and the onset of interstate conflict. We detect communities based upon weaker signals of affinity expressed in United Nations votes and speeches, as well as stronger signals observed across multiple layers of bilateral cooperation. Communities of diplomatic affinity display an expected negative relationship with conflict onset. Ties in communities based upon observed cooperation, however, display no effect under a standard model specification and a positive relationship with conflict under an alternative specification. These results align with some extant hypotheses but also point to a paucity in our understanding of the relationship between community structure and behavioral outcomes in networks.Comment: arXiv admin note: text overlap with arXiv:1802.0039

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks

Multiplex networks have become increasingly more prevalent in many fields, and have emerged as a powerful tool for modeling the complexity of real networks. There is a critical need for developing inference models for multiplex networks that can take into account potential dependencies across different layers, particularly when the aim is community detection. We add to a limited literature by proposing a novel and efficient Bayesian model for community detection in multiplex networks. A key feature of our approach is the ability to model varying communities at different network layers. In contrast, many existing models assume the same communities for all layers. Moreover, our model automatically picks up the necessary number of communities at each layer (as validated by real data examples). This is appealing, since deciding the number of communities is a challenging aspect of community detection, and especially so in the multiplex setting, if one allows the communities to change across layers. Borrowing ideas from hierarchical Bayesian modeling, we use a hierarchical Dirichlet prior to model community labels across layers, allowing dependency in their structure. Given the community labels, a stochastic block model (SBM) is assumed for each layer. We develop an efficient slice sampler for sampling the posterior distribution of the community labels as well as the link probabilities between communities. In doing so, we address some unique challenges posed by coupling the complex likelihood of SBM with the hierarchical nature of the prior on the labels. An extensive empirical validation is performed on simulated and real data, demonstrating the superior performance of the model over single-layer alternatives, as well as the ability to uncover interesting structures in real networks