Beyond Centrality - Classifying Topological Significance Using Backup Efficiency and Alternative Paths

In complex networks characterized by broad degree distribution, node significance is often associated with its degree or with centrality metrics which relate to its reachability and shortest paths passing through it. Such measures do not consider availability of efficient backup of the node and thus often fail to capture its contribution to the functionality and resilience of the network operation. In this paper we suggest the Quality of Backup (QoB) and Alternative Path Centrality (APC) measures as complementary methods which enable analysis of node significance in a manner which considers backup. We examine the theoretical significance of these measures and use them to classify nodes in social interaction networks and in the Internet AS graph while applying the valley-free routing restrictions which reflect the economic relationships between the AS nodes in the Internet. We show that both node degree and node centrality are not necessarily evidence of its significance. In particular, we show that social structures do not necessarily depend on highly central nodes and that medium degree nodes with medium centrality measure prove to be crucial for efficient routing in the Internet AS graph.