Correlations between Centrality Measures for Mobile Ad hoc Networks

Correlations between Centrality Measures for Mobile Ad hoc Networks

Natarajan Meghanathan (Jackson State University Jackson, MS, USA)
DOI: 10.4018/IJWNBT.2015040102
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The author conducts an extensive correlation coefficient analysis of four prominent centrality measures for mobile ad hoc networks. The centrality measures considered are the degree-based degree centrality and eigenvector centrality, and the shortest path-based betweenness centrality and closeness centrality. The author evaluates the correlation coefficient between any two of the above four centrality measures as a function of network connectivity and node mobility. He observes a consistent ranking (with respect to the correlation coefficients) among the pairs of centrality measures for all levels of network connectivity, node mobility and across the duration of the simulation session. The shortest path-based closeness centrality measure exhibits high correlation with the degree-based centrality measures, whereas the betweenness centrality exhibits relatively weak correlation with the degree-based centrality measures. For a given level of node mobility and network connectivity, the author does not observe the correlation coefficient values between any two centrality measures to significantly change with time.
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1. Introduction

A mobile ad hoc network (MANET) is a wireless network wherein the nodes move randomly (and often independent of each other) and the topology of the network changes dynamically with time (Murthy & Manoj, 2004). As the nodes operate within a limited transmission range, communication between any two nodes in MANETs is typically through one or more intermediate nodes. Several protocols have been proposed for unicast (Johnson & Maltz, 1996; Perkins & Royer, 1999), multicast (Wu & Tay, 1999; Mnaouer et. al., 2007) and broadcast (Dai & Wu, 2004; Saha et. al., 2010) communication in MANETs. A salient characteristic of these protocols is to optimize one or more performance metrics (relevant to the type of communication being targeted) through appropriate selection of the intermediate nodes that facilitate the communication. The measures typically used to select the intermediate nodes are hop count, node degree, neighborhood density (the sum of degrees of neighbors), residual energy at the nodes, node velocity, queue length at the nodes, etc. The design of a MANET communication protocol is typically done by considering the appropriate node selection measure considered to be directly related to the performance metric the protocol intends to optimize. For example, shortest path protocols are designed by choosing intermediate nodes that would minimize the hop count between the source-destination pair (Johnson & Maltz, 1996; Perkins & Royer, 1999); connected dominating sets (Cormen et. al., 2009) for network-wide broadcasts are determined by choosing nodes with a larger degree so that the number of constituent nodes for the CDS is as minimum as possible (to reduce the number of retransmissions) (Meghanathan, 2012; Meghanathan & Dasari, 2013); a stability-based multicast protocol (Meghanathan et. al., 2009) is designed by giving preference to go through intermediate nodes that have a relatively lower velocity, etc. Though there are some works that have analyzed the correlation coefficient between different performance metrics (for example, the average path duration and throughput in Sadagopan et. al., 2003), to the best of our knowledge, we have not come across any work that has conducted correlation coefficient analysis between the different node selection measures so that the communication protocols can choose a related measure in lieu of the commonly used measure in case the two measures have been observed to have high correlation in a MANET session. In this paper, we take the first step in this direction by analyzing the correlation coefficient between measures that are characteristic of the node degree and shortest paths.

Centrality measures are widely used in the analysis of complex networks (Newman, 2010). However, to the best of our knowledge, centrality measures (other than degree centrality) have not been used in the design of MANET communication protocols and their analysis. Centrality measures could be used to rank the importance of a node in the network with respect to one or more structural characteristics of the network. There could be two broad categories of centrality measures: degree-based and shortest path-based. Degree centrality (DegC) and Eigenvector centrality (EVC) are the two commonly used degree-based centrality measures, while Betweenness centrality (BWC) and Closeness centrality (ClC) are the two commonly used shortest path-based centrality measures. The degree centrality of a node is simply the number of neighbors for the node; the eigenvector centrality of a node is a measure of the degree of the node as well as the degree of its neighbors. For example, if two nodes u and v have the same degree, but if the neighbors of u have a relatively higher degree than the neighbors of v, then node u will have a higher EVC than node v. The betweenness centrality of a node u is a measure of the number of shortest paths between any two nodes in the network that go through u. Closeness centrality of a node is a measure of the sum of the number of hops on the shortest paths from the node to every other node in the network.

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