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Network community detection often relies on optimizing partition quality functions, like modularity. This optimization appears to be a complex problem traditionally relying on discrete heuristics. And although the problem could be…
In this paper, we first discuss the definition of modularity (Q) used as a metric for community quality and then we review the modularity maximization approaches which were used for community detection in the last decade. Then, we discuss…
In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been shown that the utility function of many machine learning applications,…
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 detection in graphs has been the subject of many algorithms. Recent methods want to optimize a modularity function which shows a maximum of relationships within communities and found a minimum of inter-community relations. these…
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…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…
The problem of maximizing a non-negative submodular function was introduced by Feige, Mirrokni, and Vondrak [FOCS'07] who provided a deterministic local-search based algorithm that guarantees an approximation ratio of $\frac 1 3$, as well…
Modularity maximization has been a fundamental tool for understanding the community structure of a network, but the underlying optimization problem is nonconvex and NP-hard to solve. State-of-the-art algorithms like the Louvain or Leiden…
Graph clustering is an important unsupervised learning technique for partitioning graphs with attributes and detecting communities. However, current methods struggle to accurately capture true community structures and intra-cluster…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted…
A basic question in network community detection is how modular a given network is. This is usually addressed by evaluating the quality of partitions detected in the network. The Girvan-Newman (GN) modularity function is the standard way to…
A "quantitative function" for community detection called modularity density has been proposed by Li, Zhang, Wang, Zhang, and Chen in $[$Phys. Rev. E 77, 036109 (2008)$]$. We study the modularity density maximization problem and we discuss…
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…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
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.…
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…
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…
The virtualization and softwarization of modern computer networks introduces interesting new opportunities for a more flexible placement of network functions and middleboxes (firewalls, proxies, traffic optimizers, virtual switches, etc.).…