Maximizing Algebraic Connectivity via Minimum Degree and Maximum Distance

Algebraic connectivity, the second smallest eigenvalue of the graph Laplacian matrix, is a fundamental performance measure in various network systems, such as multi-agent networked systems. Here, we focus on how to add an edge to a network to increase network connectivity and robustness by maximizing the algebraic connectivity. Most efficient algorithms for maximizing algebraic connectivity need to calculate it directly, which results in high time complexity, especially for large networks. We present a heuristic algorithm, the minimum degree and maximum distance algorithm, based on the analysis of the Fiedler vector, which does not need to compute the algebraic connectivity. The proposed algorithm is tested in large random networks and networks of autonomous systems peering information. The results show that it is effective and can achieve shorter running times than other algorithms. Hence, it can be applied to very large networks, especially to large sparse networks.