Computing Well-Balanced Spanning Trees of Unweighted Networks

A spanning tree of a network or graph is a subgraph that connects all nodes with the minimum number or total weight of edges. Spanning trees are among the simplest yet most effective techniques for network simplification, sampling, and uncovering a network’s backbone or skeleton. Prim’s algorithm and Kruskal’s algorithm are well-known algorithms for computing a spanning tree of a weighted network, and are therefore also the default procedure for unweighted networks in the most popular network libraries. In this paper, we empirically evaluate the performance of these algorithms on unweighted networks and compare them with priority-first search algorithms. We show that the distances between the nodes are better preserved by a simpler algorithm based on breadth-first search. The spanning trees are also more compact and well-balanced, as measured by classical graph indices. We support our findings with experiments on synthetic graphs and over a thousand real networks, and demonstrate the practical applications of the computed spanning trees. We conclude that for preserving the structure of an unweighted network, the breadth-first search algorithm should be the preferred choice.