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Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other.…
A principled approach to characterize the hidden structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for…
Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…
Motivated by multi-subject experiments in neuroimaging studies, we develop a modeling framework for joint community detection in a group of related networks, which can be considered as a sample from a population of networks. The proposed…
The stochastic block model is widely used to generate graphs with a community structure, but no simple alternative currently exists for hypergraphs, in which more than two nodes can be connected together through a hyperedge. We discuss here…
The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to…
In this paper, we introduce a hierarchical extension of the stochastic blockmodel to identify multilevel community structures in networks. We also present a Markov chain Monte Carlo (MCMC) and a variational Bayes algorithm to fit the model…
The analysis of small recurrent substructures, so called network motifs, has become a standard tool of complex network science to unveil the design principles underlying the structure of empirical networks. In many natural systems network…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
A multilevel network is defined as the junction of two interaction networks, one level representing the interactions between individuals and the other the interactions between organizations. The levels are linked by an affiliation…
Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity…
Blockmodels are a foundational tool for modeling community structure in networks, with the stochastic blockmodel (SBM), degree-corrected blockmodel (DCBM), and popularity-adjusted blockmodel (PABM) forming a natural hierarchy of increasing…
Many approaches have been proposed to discover clusters within networks. Community finding field encompasses approaches which try to discover clusters where nodes are tightly related within them but loosely related with nodes of other…
Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society. One crucial step when studying the structure and dynamics of…
Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering…
One of the most important concepts in biological network analysis is that of network motifs, which are patterns of interconnections that occur in a given network at a frequency higher than expected in a random network. In this work we are…
Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying…
Community detection in multi-layer networks has emerged as a crucial area of modern network analysis. However, conventional approaches often assume that nodes belong exclusively to a single community, which fails to capture the complex…
In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM),…
Stochastic Block Models (SBMs) are a popular approach to modeling single real-world graphs. The key idea of SBMs is to partition the vertices of the graph into blocks with similar edge densities within, as well as between different blocks.…