  The study of the topological structure of complex networks has fascinated
researchers for several decades, and today we have a fairly good understanding
of the types and reoccurring characteristics of many different complex
networks. However, surprisingly little is known today about models to compare
complex graphs, and quantitatively measure their similarity. This paper
proposes a natural similarity measure for complex networks: centrality
distance, the difference between two graphs with respect to a given node
centrality. Centrality distances allow to take into account the specific roles
of the different nodes in the network, and have many interesting applications.
As a case study, we consider the closeness centrality in more detail, and show
that closeness centrality distance can be used to effectively distinguish
between randomly generated and actual evolutionary paths of two dynamic social
networks.
