Heuristic algorithms for tree-depth of social networks

The tree-depth of a graph G is the minimum height of any rooted forest F such that G ⊆ closure(F). We implemented a dynamic programming algorithm for finding the minimum tree-depth and designed heuristic algorithms by using betweenness, closeness, triangle, and degree centralities. We also proposed a heuristic algorithm based on the tree-depth decomposition tree for the graph coloring problem. We studied some cases that our heuristic algorithm is much better than the degree first method.