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In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…
This paper addresses the problem of mixed-membership estimation in networks, where the goal is to efficiently estimate the latent mixed-membership structure from the observed network. Recognizing the widespread availability and valuable…
We introduce a metric space of clusterings, where clusterings are described by a binary vector indexed by the vertex-pairs. We extend this geometry to a hypersphere and prove that maximizing modularity is equivalent to minimizing the…
Dynamic community detection is crucial for elucidating the temporal evolution of social structures, information dissemination, and interactive behaviors within complex networks. Nonnegative matrix factorization provides an efficient…
An important step in unveiling the relation between network structure and dynamics defined on networks is to detect communities, and numerous methods have been developed separately to identify community structure in different classes of…
An optimization framework is presented for minimizing the energy functional developed around a generalized equation governing physical systems such as fluid dynamics, particle transport, phase transition, and other related systems. The…
Community detection using both graphs and social networks is the focus of many algorithms. Recent methods aimed at optimizing the so-called modularity function proceed by maximizing relations within communities while minimizing…
Community structure represents the local organization of complex networks and the single most important feature to extract functional relationships between nodes. In the last years, the problem of community detection has been reformulated…
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 propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of…
In this paper we present a novel strategy to discover the community structure of (possibly, large) networks. This approach is based on the well-know concept of network modularity optimization. To do so, our algorithm exploits a novel…
The most widely used techniques for community detection in networks, including methods based on modularity, statistical inference, and information theoretic arguments, all work by optimizing objective functions that measure the quality of…
Graph Neural Networks (GNNs) can be trained to detect communities within a graph by learning from the duality of feature and connectivity information. Currently, the common approach for optimisation of GNNs is to use comparisons to…
Detecting communities in a network, based only on the adjacency matrix, is a problem of interest to several scientific disciplines. Recently, Zhang and Moore have introduced an algorithm in [P. Zhang and C. Moore, Proceedings of the…
Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret…
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…
Modularity maximization is the most popular technique for the detection of community structure in graphs. The resolution limit of the method is supposedly solvable with the introduction of modified versions of the measure, with tunable…
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…
A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…
Community detection is one of the pivotal tools for discovering the structure of complex networks. Majority of community detection methods rely on optimization of certain quality functions characterizing the proposed community structure.…