Katz centrality

About: Katz centrality is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 77858 citations.

Strong structural control centrality of a complex network

Abstract: We introduce the definition of strong structural control centrality, which represents the dimension of strong structurally controllable subspace or the capability of a single node to control an entire directed and weighted network in a strongly structural manner. A purely algebraic algorithm to calculate strong structural control centrality is proposed. Then we explore the quality of the strong structural control centrality. The relation between strong structural control centrality and the layer index in a directed tree inspires us to research (1) some fast methods to achieve strong structural control centrality and (2) the size relationship of strong structural control centralities of nodes belonging to different supernodes.

Hirsch index as a network centrality measure

Abstract: We study the h Hirsch index as a local node centrality measure for complex networks in general. The h index is compared with the Degree centrality (a local measure), the Betweenness and Eigenvector centralities (two non-local measures) in the case of a biological network (Yeast interaction protein-protein network) and a linguistic network (Moby Thesaurus II) as test environments. In both networks, the Hirsch index has poor correlation with Betweenness centrality but correlates well with Eigenvector centrality, specially for the more important nodes that are relevant for ranking purposes, say in Search Machine Optimization. In the thesaurus network, the h index seems even to outperform the Eigenvector centrality measure as evaluated by simple linguistic criteria.

On centrality functions of a graph

Abstract: For a connected nondirected graph, a centrality function is a real valued function of the vertices defined as a linear combination of the numbers of the vertices classified according to the distance from a given vertex. Some fundamental properties of the centrality functions and the set of central vertices are summarized. Inserting an edge between a center and a vertex, the stability of the set of central vertices are investigated.

Random-Radius Ball Method for Estimating Closeness Centrality

Abstract: In the analysis of real-world complex networks, identifying important vertices is one of the most fundamental operations. A variety of centrality measures have been proposed and extensively studied in various research areas. Many of distance-based centrality measures embrace some issues in treating disconnected networks, which are resolved by the recently emerged harmonic centrality. This paper focuses on a family of centrality measures including the harmonic centrality and its variants, and addresses their computational difficulty on very large graphs by presenting a new estimation algorithm named the random-radius ball (RRB) method. The RRB method is easy to implement, and a theoretical analysis, which includes the time complexity and error bounds, is also provided. The effectiveness of the RRB method over existing algorithms is demonstrated through experiments on real-world networks.

KATZ centrality with biogeography-based optimization for influence maximization problem

Abstract: In the field of social networks, the Influence Maximization Problem (IMP) is one of the most well-known issues that have attracted many researchers in recent years. Influence Maximization (IM) means trying to find the best subset of K nodes that maximizes the number of nodes influenced by this subset. The IM is an NP-hard problem that plays an important role in viral marketing and dissemination of information. The existing solutions like greedy approaches to solving IMP do not have the efficiency and accuracy in solving the problem. In this paper, we propose a new metaheuristic algorithm based on Katz centrality with biogeography-based optimization to solve IMP in the social network. In the proposed algorithm, each habitat with the subset of K nodes is considered as the solution to the IM problem. In the proposed algorithm, the Katz centrality of each node is calculated and used as the emigration rate of each habitat. The focus of the study has been on improving the performance of the BBO algorithm by combining it with the Katz centrality. The objective was to use an enhanced meta-heuristic algorithm with measuring centrality to solve the IM problem. In the results of experiments based on different types of real-world social networks, it is well known that the proposed algorithm is more efficient, accurate, and faster than influence maximization greedy approaches.