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In large networks, using the length of shortest paths as the distance measurehas shortcomings. A well-studied shortcoming is that extending it todisconnected graphs and directed graphs is controversial. The secondshortcoming is that a huge number of vertices may have exactly the same score.The third shortcoming is that in many applications, the distance between twovertices not only depends on the length of shortest paths, but also on thenumber of shortest paths. In this paper, first we develop a new distancemeasure between vertices of a graph that yields discriminative distance-basedcentrality indices. This measure is proportional to the length of shortestpaths and inversely proportional to the number of shortest paths. We presentalgorithms for exact computation of the proposed discriminative indices.Second, we develop randomized algorithms that precisely estimate averagediscriminative path length and average discriminative eccentricity and showthat they give $(\epsilon,\delta)$-approximations of these indices. Third, weperform extensive experiments over several real-world networks from differentdomains. In our experiments, we first show that compared to the traditionalindices, discriminative indices have usually much more discriminability. Then,we show that our randomized algorithms can very precisely estimate averagediscriminative path length and average discriminative eccentricity, using onlyfew samples. Then, we show that real-world networks have usually a tiny averagediscriminative path length, bounded by a constant (e.g., 2). Fourth, in orderto better motivate the usefulness of our proposed distance measure, we presenta novel link prediction method, that uses discriminative distance to decidewhich vertices are more likely to form a link in future, and show its superiorperformance compared to the well-known existing measures.

Discriminative Distance-Based Network Indices with Application to Link Prediction