[Paper Review] Improving information centrality of a node in complex networks by adding edges

Liren Shan, Yuhao Yi+1 more|arXiv (Cornell University)|Apr 18, 2018

Complex Network Analysis Techniques17 references3 citations

TL;DR

This paper proposes a greedy algorithm to maximize the information centrality of a target node in complex networks by adding k new edges incident to it. By reformulating the problem as minimizing resistance distance, the authors prove the objective is monotone and supermodular, enabling a (1−1/e)-approximation algorithm with O(n³) time complexity and a faster (1−1/e−ε)-approximation variant with Õ(mkε⁻²) time, both validated on real and synthetic networks with superior performance.

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 $\left(1-\frac{1}{e} ight)$ and $O(n^3)$ running time. To speed up the computation, we also present an algorithm to compute $\left(1-\frac{1}{e}-ε ight)$-approximate resistance distance $\mathcal{R}_v$ after iteratively adding $k$ edges, the running time of which is $\widetilde{O} (mkε^{-2})$ for any $ε>0$, where the $\widetilde{O} (\cdot)$ notation suppresses the ${ m poly} (\log n)$ factors. We experimentally demonstrate the effectiveness and efficiency of our proposed algorithms.

Motivation & Objective

• To address the gap in optimizing information centrality via edge addition, a metric with better discriminating power than betweenness and closeness centrality.
• To formulate the problem of maximizing information centrality I_v as minimizing resistance distance R_v between the target node v and all other nodes.
• To design efficient approximation algorithms that achieve high-quality solutions under practical time constraints.
• To validate the effectiveness and efficiency of the proposed algorithms on real-world and model networks.

Proposed method

• Reformulate the problem of maximizing information centrality I_v as minimizing the resistance distance R_v, which is the sum of effective resistances between node v and all other nodes.
• Prove that the objective function is monotone and supermodular, enabling the use of greedy approximation algorithms with theoretical guarantees.
• Propose a first greedy algorithm that iteratively adds one edge at a time to minimize R_v, achieving a (1−1/e)-approximation in O(n³) time.
• Introduce a faster approximation algorithm using randomized resistance distance estimation, achieving (1−1/e−ε)-approximation in Õ(mkε⁻²) time with polylogarithmic factors suppressed.
• Use the Laplacian matrix and effective resistance computations to efficiently evaluate the impact of each candidate edge addition.
• Implement both algorithms and compare them against baselines such as random, top-degree, and top-centrality edge insertion strategies.

Experimental results

Research questions

• RQ1 Can we efficiently maximize the information centrality of a specific node in a network by adding k new edges incident to it?
• RQ2 Is the problem of minimizing resistance distance R_v via k edge additions monotone and supermodular, enabling approximation guarantees?
• RQ3 What is the trade-off between solution quality and computational efficiency in scaling this problem to large networks?
• RQ4 How do the proposed greedy algorithms compare to baseline strategies like random, degree-based, or centrality-based edge insertion?

Key findings

• The proposed (1−1/e)-approximation algorithm achieves high solution quality with O(n³) time complexity, making it suitable for medium-sized networks.
• The faster Õ(mkε⁻²) algorithm achieves a (1−1/e−ε)-approximation and scales effectively to massive networks, such as com-DBLP and roadNet-TX, where the exact method fails due to high time complexity.
• On all tested real and synthetic networks, the greedy algorithms significantly outperform random, top-degree, and top-centrality baselines in increasing the target node's information centrality.
• For networks like Facebook and Powergrid, the approximation algorithm achieves over 99% of the information centrality score of the exact method while being orders of magnitude faster.
• The average running time of the approximation algorithm is less than 10% of the exact method on large networks, with the ratio of information centrality scores consistently above 0.99.
• The results demonstrate that edge addition strategies based on resistance distance minimization are more effective than degree- or centrality-based heuristics for improving information centrality.