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Community structures are an important feature of many social, biological and technological networks. Here we study a variation on the method for detecting such communities proposed by Girvan and Newman and based on the idea of using…
Identifying community structure can be a potent tool in the analysis and understanding of the structure of complex networks. Up to now, methods for evaluating the performance of identification algorithms use ad-hoc networks with communities…
The analysis and detection of communities in network structures are becoming increasingly relevant for understanding social behavior. One of the principal challenges in this field is the complexity of existing algorithms. The Girvan-Newman…
In dynamic complex networks, entities interact and form network communities that evolve over time. Among the many static Community Detection (CD) solutions, the modularity-based Louvain, or Greedy Modularity Algorithm (GMA), is widely…
We consider a non-projective class of inhomogeneous random graph models with interpretable parameters and a number of interesting asymptotic properties. Using the results of Bollob\'as et al. [2007], we show that i) the class of models is…
Different kinds of random walks have proven to be useful in the study of structural properties of complex networks. Among them, the restricted dynamics of self-avoiding random walks (SAW), which visit only at most once each vertex in the…
In this paper, we proposed a novel two-stage optimization method for network community partition, which is based on inherent network structure information. The introduced optimization approach utilizes the new network centrality measure of…
Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a…
We present an empirical study of different social networks obtained from digital repositories. Our analysis reveals the community structure and provides a useful visualising technique. We investigate the scaling properties of the community…
This work will appear as a chapter in a forthcoming volume titled `Topics in Probabilistic Graph Theory'. For a given graph $G$, each partition of the vertices has a modularity score, with higher values indicating that the partition better…
There are several metrics (Modularity, Mutual Information, Conductance, etc.) to evaluate the strength of graph clustering in large graphs. These metrics have great significance to measure the effectiveness and they are often used to find…
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…
We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis,…
Community analysis algorithm proposed by Clauset, Newman, and Moore (CNM algorithm) finds community structure in social networks. Unfortunately, CNM algorithm does not scale well and its use is practically limited to networks whose sizes…
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…
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…
This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor.…
One of the best-known models in network science is preferential attachment. In this model, the probability of attaching to a node depends on the degree of all nodes in the population, and thus depends on global information. In many…
Finding groups of connected individuals in large graphs with tens of thousands or more nodes has received considerable attention in academic research. In this paper, we analyze three main issues with respect to the recent influx of papers…
Much effort has gone into understanding the modular nature of complex networks. Communities, also known as clusters or modules, are typically considered to be densely interconnected groups of nodes that are only sparsely connected to other…