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Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed for their analysis. Naturally, the…

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…

Because networks can be used to represent many complex systems, they have attracted considerable attention in physics, computer science, sociology, and many other disciplines. One of the most important areas of network science is the…

In the last few years many real-world networks have been found to show a so-called community structure organization. Much effort has been devoted in the literature to develop methods and algorithms that can efficiently highlight this hidden…

We study networks that display community structure -- groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence…

The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this…

With invaluable theoretical and practical benefits, the problem of partitioning networks for community structures has attracted significant research attention in scientific and engineering disciplines. In literature, Newman's modularity…

Community detection, the decomposition of a graph into essential building blocks, has been a core research topic in network science over the past years. Since a precise notion of what constitutes a community has remained evasive, community…

We propose a novel method to find the community structure in complex networks based on an extremal optimization of the value of modularity. The method outperforms the optimal modularity found by the existing algorithms in the literature. We…

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. Clustering, community structure and assortative mixing by degree are perhaps among most prominent…

Community detection is a key tool for analyzing the structure of large networks. Standard methods, such as modularity optimization, focus on identifying densely connected groups but often overlook natural local separations in the graph. In…

Graphs representing real world systems may be studied from their underlying community structure. A community in a network is an intuitive idea for which there is no consensus on its objective mathematical definition. The most used metric in…

Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature,…

Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…

In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…

This paper investigates community detection by modularity maximisation on bipartite networks. In particular we are interested in how the operation of projection, using one node set of the bipartite network to infer connections between nodes…

Detecting community structure is fundamental to clarify the link between structure and function in complex networks and is used for practical applications in many disciplines. A successful method relies on the optimization of a quantity…

In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…

Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…

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.…