As the Internet becomes the social infrastructure, a network design method that has the adaptability against the failure of network equipment and has the sustainability against changes of traffic demand is becoming important. Since we do not know in advance when the environmental changes occur and how large the changes are, it is preferable to have heterogeneity in topological structures so that the network can evolve more easily. In this paper, we investigate the heterogeneity of topological

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... ructures by using mutual information of remaining degree. Our results show that the mutual information is high at the most of router-level topologies, which indicate that the route-level topologies are highly designed by, e.g., the network operators. We then discuss and show that the mutual information represents the heterogeneity of topological structure through illustrative examples.