Improving information centrality of a node in complex networks by adding edges

Abstract

The problem of increasing the centrality of a network node arises in many practical applications. In this paper, we study the optimization problem of maximizing the information centrality $I_v$ of a given node $v$ in a network with $n$ nodes and $m$ edges, by creating $k$ new edges incident to $v$. Since $I_v$ is the reciprocal of the sum of resistance distance ${\mathcal{R}}_v$ between $v$ and all nodes, we alternatively consider the problem of minimizing ${\mathcal{R}}_v$ by adding $k$ new edges linked to $v$. We show that the objective function is monotone and supermodular. We provide a simple greedy algorithm with an approximation factor $\left(1-\frac{1}{e}\right)$ and $O(n^3)$ running time. To speed up the computation, we also present an algorithm to compute $\left(1-\frac{1}{e}-ϵ\right)$-approximate resistance distance ${\mathcal{R}}_v$ after iteratively adding $k$ edges, the running time of which is $\tilde{O}(mk{ϵ}^{-2})$ for any $ϵ>0$, where the $\tilde{O}(\cdot )$ notation suppresses the $\mathrm{poly}(\log n)$ factors. We experimentally demonstrate the effectiveness and efficiency of our proposed algorithms.