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In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
The structure entropy is an important index to illuminate the structure property of the complex network. Most of the existing structure entropies are based on the degree distribution of the complex network. But the structure entropy based…
Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually…
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…
The betweenness centrality (BC) is an important quantity for understanding the structure of complex large networks. However, its calculation is in general difficult and known in simple cases only. In particular, the BC has been exactly…
Network science provides an indispensable theoretical framework for studying the structure and function of real complex systems. Different network models are often used for finding the rules that govern their evolution, whereby the correct…
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…
Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of…
We analyze the betweenness centrality (BC) of nodes in large complex networks. In general, the BC is increasing with connectivity as a power law with an exponent $\eta$. We find that for trees or networks with a small loop density $\eta=2$…
Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to…
The roles of different nodes within a network are often understood through centrality analysis, which aims to quantify the capacity of a node to influence, or be influenced by, other nodes via its connection topology. Many different…
We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
We study a supremacy distribution in evolving Barabasi-Albert networks. The supremacy $s_i$ of a node $i$ is defined as a total number of all nodes that are younger than $i$ and can be connected to it by a directed path. For a network with…
We propose a novel measure to assess the presence of meso-scale structures in complex networks. This measure is based on the identification of regular patterns in the adjacency matrix of the network, and on the calculation of the quantity…
Betweenness centrality (BC) is one of the most used centrality measures for network analysis, which seeks to describe the importance of nodes in a network in terms of the fraction of shortest paths that pass through them. It is key to many…
Complex networks provide a powerful mathematical representation of complex systems in nature and society. To understand complex networks, it is crucial to explore their internal structures, also called structural regularities. The task of…
The structure entropy is one of the most important parameters to describe the structure property of the complex networks. Most of the existing struc- ture entropies are based on the degree or the betweenness centrality. In order to describe…
A very interesting matter of Network Science is assessing how complex a given network is. In other words, by how much does such a network departs from any general patterns which could be evoked for its description. Among other choices,…
The identification of nodes occupying important positions in a network structure is crucial for the understanding of the associated real-world system. Usually, betweenness centrality is used to evaluate a node capacity to connect different…