Related papers: The modularity of random graphs on the hyperbolic …
The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to…
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.…
We consider a model for complex networks that was recently proposed as a model for complex networks by Krioukov et al. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
We consider Gallai's graph Modular Decomposition theory for network analytics. On the one hand, by arguing that this is a choice tool for understanding structural and functional similarities among nodes in a network. On the other, by…
We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence, small distances and clustering, features that are…
We present a compact matrix formulation of the modularity, a commonly used quality measure for the community division in a network. Using this formulation we calculate the density of modularities, a statistical measure of the probability of…
Numerous networked systems feature a structure of nontrivial communities, which often correspond to their functional modules. Such communities have been detected in real-world biological, social and technological systems, as well as in…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
Real-data networks often appear to have strong modularity, or network-of-networks structure, in which subgraphs of various size and consistency occur. Finding the respective subgraph structure is of great importance, in particular for…
The clustering property of complex networks indicates the abundance of small dense subgraphs in otherwise sparse networks. For a community-affiliation network defined by a superposition of Bernoulli random graphs, which has a nonvanishing…
Given a graph of interactions, a module (also called a community or cluster) is a subset of nodes whose fitness is a function of the statistical significance of the pairwise interactions of nodes in the module. The topic of this paper is a…
We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…
Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network…
We characterize the large-sample properties of network modularity in the presence of covariates, under a natural and flexible nonparametric null model. This provides for the first time an objective measure of whether or not a particular…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
Modularity is a widely used measure for evaluating community structure in networks. The definition of modularity involves a comparison of within-community edges in the observed network and that number in an equivalent randomized network.…
In network science, a group of nodes connected with each other at higher probability than with those outside the group is referred to as a community. From the perspective that individual communities are associated with functional modules…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…