06033185

j

06033185 Vernitski, Alexei Pyatkin, Artem Astral graphs (threshold graphs), scale-free graphs and related algorithmic questions. J. Discrete Algorithms 12, 24-28 (2012). 2012 Elsevier Science B.V., Amsterdam EN scale-free graph threshold graph NP-complete problem clustering coefficient

doi:10.1016/j.jda.2011.06.003

Summary: The astral index of a graph is defined as the smallest number of astral graphs (also known as threshold graphs) into which the graph can be decomposed, divided by the number of vertices in the graph. The astral index is a promising new graph measure for analysing the structure of graphs in applications. In this paper, we prove some theoretical results concerning astral graphs and the astral index. We reveal a connection between astral graphs and scale-free graphs. We prove that finding the exact value of the astral index is an NP-complete problem.