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Using an intuitive concept of what constitutes a meaningful community, a novel metric is formulated for detecting non-overlapping communities in undirected, weighted heterogeneous networks. This metric, modularity density, is shown to be…
Many real systems can be represented as networks whose analysis can be very informative regarding the original system's organisation. In the past decade community detection received a lot of attention and is now an active field of research.…
We study networks that display community structure -- groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence…
Community structures are an important feature of many social, biological and technological networks. Here we study a variation on the method for detecting such communities proposed by Girvan and Newman and based on the idea of using…
Recently network analysis has gained more and more attentions in statistics, as well as in computer science, probability, and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic…
Identifying community structure in networks is an issue of particular interest in network science. The modularity introduced by Newman and Girvan [Phys. Rev. E 69, 026113 (2004)] is the most popular quality function for community detection…
Temporal Networks, and more specifically, Markovian Temporal Networks, present a unique challenge regarding the community discovery task. The inherent dynamism of these systems requires an intricate understanding of memory effects and…
Recent research has shown that virtually all algorithms aimed at the identification of communities in networks are affected by the same main limitation: the impossibility to detect communities, even when these are well-defined, if the…
We investigate signed networks with community structure with respect to their spectrum and their evolution under a dynamical model of structural balance, a prominent theory of signed social networks. The spectrum of the adjacency matrix…
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…
Community structure is an important structural property that extensively exists in various complex networks. In the past decade, much attention has been paid to the design of community-detection methods, but analyzing the behaviors of the…
The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle…
We develop a principled methodology to infer assortative communities in networks based on a nonparametric Bayesian formulation of the planted partition model. We show that this approach succeeds in finding statistically significant…
We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeable networks. Conditional on latent (unobserved) variables, the edges of the network are generated by their finite growth history…
We present a simple and flexible method to prove consistency of semidefinite optimization problems on random graphs. The method is based on Grothendieck's inequality. Unlike the previous uses of this inequality that lead to constant…
We demonstrate an exact equivalence between two widely used methods of community detection in networks, the method of modularity maximization in its generalized form which incorporates a resolution parameter controlling the size of the…
Networks are a widely-used tool to investigate the large-scale connectivity structure in complex systems and graphons have been proposed as an infinite size limit of dense networks. The detection of communities or other meso-scale…
The study of network structure is pervasive in sociology, biology, computer science, and many other disciplines. One of the most important areas of network science is the algorithmic detection of cohesive groups of nodes called…
Community detection in networks is the process of identifying unusually well-connected sub-networks and is a central component of many applied network analyses. The paradigm of modularity optimization stipulates a partition of the network's…
We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…