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We study community structure of networks. We have developed a scheme for maximizing the modularity Q based on mean field methods. Further, we have defined a simple family of random networks with community structure; we understand the…
Network sparsification aims to reduce the number of edges of a network while maintaining its structural properties; such properties include shortest paths, cuts, spectral measures, or network modularity. Sparsification has multiple…
Study of the cluster- or community structure of complex networks makes an important contribution to the understanding of networks at a functional level. Despite the many efforts, no definition of community has been agreed on and important…
Complex networks represent interactions between entities. They appear in various contexts such as sociology, biology, etc., and they generally contain highly connected subgroups called communities. Community detection is a well-studied…
Recently, non-convex regularisation models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies $\phi$ in the total variation type functional…
We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges…
Networks with node covariates offer two advantages to community detection methods, namely, (i) exploit covariates to improve the quality of communities, and more importantly, (ii) explain the discovered communities by identifying the…
Graph theoretical analysis of the community structure of networks attempts to identify the communities (or modules) to which each node affiliates. However, this is in most cases an ill-posed problem, as the affiliation of a node to a single…
The Artificial Benchmark for Community Detection (ABCD) graph is a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the…
Agglomerative clustering is a well established strategy for identifying communities in networks. Communities are successively merged into larger communities, coarsening a network of actors into a more manageable network of communities. The…
The issue of network community detection has been extensively studied across many fields. Most community detection methods assume that nodes belong to only one community. However, in many cases, nodes can belong to multiple communities…
Given the ubiquity of modularity in biological systems, module-level regulation analysis is vital for understanding biological systems across various levels and their dynamics. Current statistical analysis on biological modules…
Many recent advances in computer vision have demonstrated the impressive power of dense and nonsubmodular energy functions in solving visual labeling problems. However, minimizing such energies is challenging. None of existing techniques…
Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes…
Detecting communities in complex networks can shed light on the essential characteristics and functions of the modeled phenomena. This topic has attracted researchers of various fields from both academia and industry. Among the different…
The generalized version of modularity for multilayer networks, a.k.a. multislice modularity, is characterized by two model parameters, namely resolution factor and inter-layer coupling factor. The former corresponds to a notion of…
The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). Community detection in graphs is now often conducted through modularity maximization: given an undirected graph $G=(V,E)$, we are…
Many complex systems are organized in the form of a network embedded in space. Important examples include the physical Internet infrastucture, road networks, flight connections, brain functional networks and social networks. The effect of…
Most community detection algorithms from the literature work as optimization tools that minimize a given \textit{fitness function}, while assuming that each node belongs to a single community. Since there is no hard concept of what a…
Modularity, first proposed by [Newman and Girvan, 2004], is one of the most popular ways to quantify the significance of community structure in complex networks. It can serve as both a standard benchmark to compare different community…