Related papers: Modularity and random graphs
For a given graph $G$, each partition of the vertices has a modularity score, with higher values indicating that the partition better captures community structure in $G$. The modularity $q^*(G)$ of the graph $G$ is defined to be the maximum…
Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard…
Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…
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…
Modularity is a parameter indicating the presence of community structure in the graph. Nowadays it lies at the core of widely used clustering algorithms. We study the modularity of the most classical random graph, binomial $G(n,p)$. In 2020…
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…
Suppose that there is an unknown underlying graph $G$ on a large vertex set, and we can test only a proportion of the possible edges to check whether they are present in $G$. If $G$ has high modularity, is the observed graph $G'$ likely to…
One of the most relevant tasks in network analysis is the detection of community structures, or clustering. Most popular techniques for community detection are based on the maximization of a quality function called modularity, which in turn…
We relate two important notions in graph theory: expanders which are highly connected graphs, and modularity a parameter of a graph that is primarily used in community detection. More precisely, we show that a graph having modularity…
Modularity was introduced as a measure of goodness for the community structure induced by a partition of the set of vertices in a graph. Then, it also became an objective function used to find good partitions, with high success.…
Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph…
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of…
Many algorithms have been proposed for detecting disjoint communities (relatively densely connected subgraphs) in networks. One popular technique is to optimize modularity, a measure of the quality of a partition in terms of the number of…
The modularity of a network quantifies the extent, relative to a null model network, to which vertices cluster into community groups. We define a null model appropriate for bipartite networks, and use it to define a bipartite modularity.…
Current modularity-based community detection algorithms attempt to find cluster memberships that maximize modularity within a fixed graph topology. Diverging from this conventional approach, our work introduces a novel strategy that employs…
The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…
Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more.…
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…
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…
Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities…