“…Due to the wide-spread use of graphs in analysis, mining, and visualization of interconnected data, there are many definitions of the node distance and proximity. Path-length based definitions, such as those used by Palmer et al (2006), Boldi et al (2011), Cohen et al (2003), Wei (2010), Xiao et al (2009), Zhou et al (2009) , are 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 useful when the relatedness can be captured solely based on the properties of the nodes and edges on the shortest path (based on some definition of path-length). Randomwalk based definitions, such as hitting distance (Chen et al, 2008;Mei et al, 2008) and personalized PageRank (PPR) score (Balmin et al, 2004;Chakrabarti, 2007;Jeh and Widom, 2002;Tong et al, 2006a;Tong et al, 2007;Liu et al, 2013;Lofgren et al, 2014;Maehara et al, 2014), of node relatedness, on the other hand, also take into account the density of the edges: intuitively, as in path-length based definitions, a node can be said to be...…”