Attacking The Assortativity Coefficient Under A Rewiring Strategy

Degree correlation is an important characteristic of networks, which is usually quantified by the assortativity coefficient. However, concerns arise about changing the assortativity coefficient of a network when networks suffer from adversarial attacks. In this paper, we analyze the factors that affect the assortativity coefficient and study the optimization problem of maximizing or minimizing the assortativity coefficient (r) in rewired networks with $k$ pairs of edges. We propose a greedy algorithm and formulate the optimization problem using integer programming to obtain the optimal solution for this problem. Through experiments, we demonstrate the reasonableness and effectiveness of our proposed algorithm. For example, rewired edges 10% in the ER network, the assortativity coefficient improved by 60%.