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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…
A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase…
In this paper we propose weighted symmetric binary matrix factorization (wSBMF) framework to detect overlapping communities in bipartite networks, which describe relationships between two types of nodes. Our method improves performance by…
The identification of community structure in a social network is an important problem tackled in the literature of network analysis. There are many solutions to this problem using a static scenario, when facing a dynamic scenario some…
Community structure identification has been an important research topic in complex networks and there has been many algorithms proposed so far to detect community structures in complex networks, where most of the algorithms are not suitable…
We consider the complexity of random ferromagnetic landscapes on the hypercube $\{\pm 1\}^N$ given by Ising models on the complete graph with i.i.d. non-negative edge-weights. This includes, in particular, the case of Bernoulli disorder…
We develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and links orientations. Since the method detects efficiently clustered nodes in large…
A flow approach to community detection in complex network and multilayer network systems is proposed. Two methods have been developed to search for communities in a network system (NS). The first of them is based on the calculation of flow…
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.…
The paper investigates the problem of finding communities in complex network systems, the detection of which allows a better understanding of the laws of their functioning. To solve this problem, two approaches are proposed based on the use…
Many social and biological networks consist of communities - groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting…
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…
The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in…
Community structure identification has been one of the most popular research areas in recent years due to its applicability to the wide scale of disciplines. To detect communities in varied topics, there have been many algorithms proposed…
Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a new framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of…
Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…
Community structure exists in many real-world networks and has been reported being related to several functional properties of the networks. The conventional approach was partitioning nodes into communities, while some recent studies start…
We consider Ising models in two and three dimensions with nearest neighbor ferromagnetic interactions and long range, power law decaying, antiferromagnetic interactions. If the strength of the ferromagnetic coupling J is larger than a…
We consider social systems in which agents are not only characterized by their states but also have the freedom to choose their interaction partners to maximize their utility. We map such systems onto an Ising model in which spins are…
In the study of networked systems such as biological, technological, and social networks the available data are often uncertain. Rather than knowing the structure of a network exactly, we know the connections between nodes only with a…