Centrality Robustness and Link Prediction in Complex Social Networks

Abstract

This chapter addresses two important issues in social network analysis that involve uncertainty. Firstly, we present an analysis on the robustness of centrality measures that extends the work presented in Borgatti et al. using three types of complex network structures and one real social network. Secondly, we present a method to predict edges in dynamic social networks. Our experimental results indicate that the robustness of the centrality measures applied to more realistic social networks follows a predictable pattern and that the use of temporal statistics could improve the accuracy achieved on edge prediction.

Time-Dependent Variation of the Centrality Measures of the Nodes during the Evolution of a Scale-Free Network

“…The larger the value of this entry for a vertex, the higher is its ranking with respect to Eigenvector centrality. We illustrate the use of the Power Iteration method [23] (see example in Figure 2) to efficiently calculate the principal eigenvector for the adjacency matrix of a graph. The eigenvector X i+1 of a network graph at the end of the (i+1) th iteration is given by:…”

“…As can be seen in the example of Figure 2, the Eigenvector centrality values of the vertices are more likely to be distinct and could be a better measure for unambiguously ranking the vertices of a network graph. The number of iterations needed for the normalized value of the eigenvector to converge is anticipated to be less than or equal to the number of vertices in the graph [23]. Each iteration of the power iteration method requires Θ(V 2 ) multiplications, where V is the number of vertices in the graph.…”

“…Various studies (e.g., [17][18][19][20][21][22][23]) have been conducted in the literature to analyze the robustness of the centrality measures of the nodes to random and systematic variations of the network structure. While [18][19] focus on link additions and deletions only, [20][21][22] analyze the stability of the centrality measures by considering the addition and deletion of nodes for different types of network topologies such as uniform random, small-world, core-periphery, scale-free and cellular.…”

“…While [18][19] focus on link additions and deletions only, [20][21][22] analyze the stability of the centrality measures by considering the addition and deletion of nodes for different types of network topologies such as uniform random, small-world, core-periphery, scale-free and cellular. In [23], the authors examined the effects of different sampling techniques (selecting the nodes and links for addition/deletion) on the different types of complex networks with regards to the robustness of the centrality measures. The Eigenvector centrality measure was observed to be the most stable (i.e., robust) while considering node and link additions.…”