K-Core Maximization through Edge Additions

TL;DR

This paper investigates the NP-hard problem of maximizing a network's k-core by adding a limited number of edges, proposing heuristics and demonstrating their effectiveness through experiments on real datasets.

Contribution

It introduces the edge k-core maximization problem, proves its computational hardness, and develops heuristic algorithms with proven effectiveness.

Findings

Heuristic algorithms significantly improve k-core size in experiments.

The problem is NP-hard and APX-hard, indicating computational difficulty.

Experimental results on real datasets validate the proposed methods' efficiency.

Abstract

A popular model to measure the stability of a network is k-core - the maximal induced subgraph in which every vertex has at least k neighbors. Many studies maximize the number of vertices in k-core to improve the stability of a network. In this paper, we study the edge k-core problem: Given a graph G, an integer k and a budget b, add b edges to non-adjacent vertex pairs in G such that the k-core is maximized. We prove the problem is NP-hard and APX-hard. A heuristic algorithm is proposed on general graphs with effective optimization techniques. Comprehensive experiments on 9 real-life datasets demonstrate the effectiveness and the efficiency of our proposed methods.