document: Using structure indices for efficient approximation of network properties Statistics on networks have become vital to the study of relational data drawn from areas such as bibliometrics , fraud detection , bioinformatics , and the Internet . Calculating many of the most important measures - such as betweenness centrality , closeness centrality , and graph diameter-requires identifying short paths in these networks . However , finding these short paths can be intractable for even moderate-size networks . We introduce the concept of a network structure index ( NSI ) , a composition of ( 1 ) a set of annotations on every node in the network and ( 2 ) a function that uses the annotations to estimate graph distance between pairs of nodes . We present several varieties of NSIs , examine their time and space complexity , and analyze their performance on synthetic and real data sets . We show that creating an NSI for a given network enables extremely efficient and accurate estimation of a wide variety of network statistics on that network .
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