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The maximization of generalized modularity performs well on networks in which the members of all communities are statistically indistinguishable from each other. However, there is no theory bounding the maximization performance in more…
The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this…
From neuroscience and genomics to systems biology and ecology, researchers rely on clustering similarity data to uncover modular structure. Yet widely used clustering methods, such as hierarchical clustering, k-means, and WGCNA, lack…
Local network community detection aims to find a single community in a large network, while inspecting only a small part of that network around a given seed node. This is much cheaper than finding all communities in a network. Most methods…
Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. There has been a few work studying the community detection…
Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models…
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,…
One of the most widely studied problem in mining and analysis of complex networks is the detection of community structures. The problem has been extensively studied by researchers due to its high utility and numerous applications in various…
Community structure is one of the most important features of complex networks. Modularity-based methods for community detection typically rely on heuristic algorithms to optimize a specific community quality function. Such methods are…
Community detection algorithms have been widely used to study the organization of complex systems like the brain. A principal appeal of these techniques is their ability to identify a partition of brain regions (or nodes) into communities,…
We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is…
Many real-world networks, including nervous systems, exhibit meso-scale structure. This means that their elements can be grouped into meaningful sub-networks. In general, these sub-networks are unknown ahead of time and must be "discovered"…
The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…
The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale…
Community structure is prevalent in real-world networks, with empirical studies revealing heterogeneous distributions where a few dominant majority communities coexist with many smaller groups. These small-scale groups, which we term…
Communities are fundamental entities for the characterization of the structure of real networks. The standard approach to the identification of communities in networks is based on the optimization of a quality function known as…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges or as a…
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…
The study of the sub-structure of complex networks is of major importance to relate topology and functionality. Many efforts have been devoted to the analysis of the modular structure of networks using the quality function known as…