Abstract:
In this work we propose a centrality measure for networks, which we refer to as Laplacian centrality, that provides a general framework for the centrality of a vertex based on the idea that the importance (or centrality) of a vertex is related to the ability of the network to respond to the deactivation or removal of that vertex from the network. In particular, the Laplacian centrality of a vertex is defined as the relative drop of Laplacian energy caused by the deactivation of this vertex. The Laplacian energy of network Gwith nvertices is defined as , where is the eigenvalue of the Laplacian matrix of G. Other dynamics based measures such as that of Masuda and Kori and PageRank compute the importance of a node by analyzing the way paths pass through a node while our measure captures this information as well as the way these paths are “redistributed” when the node is deleted. The validity and robustness of this new measure are illustrated on two different terrorist social network data sets and 84 networks in James Moody’s Add Health in school friendship nomination data, and is compared with other standard centrality measures.

Abstract:
Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the network. By counting only shortest paths, however, the conventional definition implicitly assumes that information spreads only along those shortest paths. Here we propose a betweenness measure that relaxes this assumption, including contributions from essentially all paths between nodes, not just the shortest, although it still gives more weight to short paths. The measure is based on random walks, counting how often a node is traversed by a random walk between two other nodes. We show how our measure can be calculated using matrix methods, and give some examples of its application to particular networks.

Abstract:
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 solve analytically the network evolution. During the complete evolution, the network is characterized by nestedness: the neighbourhood of a node is contained in the neighbourhood of the nodes with larger degree. We find a discontinuous transition in the network density between hierarchical and homogeneous networks, depending on the rate of link decay. We also show that this evolution mechanism leads to double power-law degree distributions, with interrelated exponents.

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.

Abstract:
We study the lobby index (l-index for short) as a local node centrality measure for complex networks. The l-inde is compared with degree (a local measure), betweenness and Eigenvector centralities (two global measures) in the case of biological network (Yeast interaction protein-protein network) and a linguistic network (Moby Thesaurus II). In both networks, the l-index has poor correlation with betweenness but correlates with degree and Eigenvector. Being a local measure, one can take advantage by using the l-index because it carries more information about its neighbors when compared with degree centrality, indeed it requires less time to compute when compared with Eigenvector centrality. Results suggests that l-index produces better results than degree and Eigenvector measures for ranking purposes, becoming suitable as a tool to perform this task.

Abstract:
A new centrality measure for complex networks, called resource allocation centrality measure, was proposed in this paper. It can overcome some disadvantages of several often used centrality measures that can not be applicable to the disconnect networks. The resource allocation centrality of a node is defined as its amount of resource received from other nodes. If a node receives more resources from other nodes, the node is more important than others. Simulation tests on artificial networks and real networks show that the resource allocation centrality measure has good performances in detecting bridge node and has good stability.

Abstract:
In many applications we are required to increase the deployment of a distributed monitoring system on an evolving network. In this paper we present a new method for finding candidate locations for additional deployment in the network. This method is based on the Group Betweenness Centrality (GBC) measure that is used to estimate the influence of a group of nodes over the information flow in the network. The new method assists in finding the location of k additional monitors in the evolving network, such that the portion of additional traffic covered is at least (1-1/e) of the optimal.

Abstract:
Analyzing networks requires complex algorithms to extract meaningful information. Centrality metrics have shown to be correlated with the importance and loads of the nodes in network traffic. Here, we are interested in the problem of centrality-based network management. The problem has many applications such as verifying the robustness of the networks and controlling or improving the entity dissemination. It can be defined as finding a small set of topological network modifications which yield a desired closeness centrality configuration. As a fundamental building block to tackle that problem, we propose incremental algorithms which efficiently update the closeness centrality values upon changes in network topology, i.e., edge insertions and deletions. Our algorithms are proven to be efficient on many real-life networks, especially on small-world networks, which have a small diameter and a spike-shaped shortest distance distribution. In addition to closeness centrality, they can also be a great arsenal for the shortest-path-based management and analysis of the networks. We experimentally validate the efficiency of our algorithms on large networks and show that they update the closeness centrality values of the temporal DBLP-coauthorship network of 1.2 million users 460 times faster than it would take to compute them from scratch. To the best of our knowledge, this is the first work which can yield practical large-scale network management based on closeness centrality values.

Abstract:
Centrality measure is an important concept in networks. It indicates the relative importance of nodes in a network. Various centrality measures have been proposed in the literature, such as degree centrality, closeness centrality etc. Practically all these measures are some values based on the properties of the node concerned. Eigenvector centrality takes into account the centrality value of the neighbours of a node to assign a centrality value to it. In this paper, we show how this value can be utilized to select relay nodes in a delay tolerant network and improve the delivery delay.

Abstract:
Study of social networks reveal communication patterns which are of interest to researchers. Co-authorship network is one type of a social network. These networks represent the publication work carried out by researchers. Co-authorship networks analysis is useful in understanding the structure of scientific collaborations and status of individual authors. Centrality measure calculation is one of the many tasks of social network analysis. Focus of this paper work is on centrality measure analysis carried out on the co-authorship network using Gephi, a social network analysis tool.