Exploring Communities in Large Profiled Graphs

Abstract

Given a graph G and a vertex q ∈ G, the community search (CS) problem aims to efficiently find a subgraph of G whose vertices are closely related to q. Communities are prevalent in social and biological networks, and can be used in product advertisement and social event recommendation. In this paper, we study profiled community search (PCS), where CS is performed on a profiled graph. This is a graph in which each vertex has labels arranged in a hierarchical manner. Extensive experiments show that PCS can identify communities with themes that are common to their vertices, and is more effective than existing CS approaches. As a naive solution for PCS is highly expensive, we have also developed a tree index, which facilitate efficient and online solutions for PCS.

Efficient algorithms for densest subgraph discovery

“…add an edge s→v with capacity deg G (v, Ψ); 8 add an edge v→t with capacity α|V Ψ |; 9 for each (h-1)-clique ψ ∈ Λ do 10 for each vertex v ∈ ψ do 11 add an edge ψ→v with capacity +∞; 12 for each (h-1)-clique ψ ∈ Λ do 13 for each vertex v ∈ V do 14 if ψ and v form an h-clique then 15 add an edge v→ψ with capacity 1; 16 find minimum st-cut (S, T ) from the flow network F (V F , E F ); 17 if S={s} then u ← α; 18 else l ← α, D ← the subgraph induced by S\{s}; 19 return D;…”

“…Specifically, we first compute the exact clique-degree for each vertex in G[W ], and record the minimum and maximum clique-degrees (lines 6-7). Then, we perform core decomposition for G[W ] with clique-core numbers in [k l , ku] (lines [8][9][10][11][12][13][14][15], during which the maximum clique-core number kmax and (kmax, Ψ)-core are kept (lines [13][14]. After that, we double the size of W for the next iteration (line 15).…”

“…Other Dense Subgraphs. Recently, many other dense subgraph models [24], such as k-core [7,47,51,23,22,20,25,26,67,12], k-truss [15,37,69,39,38], k-(r, s) nucleus [60,58,61,59] (a generalization of k-core and k-truss), k-clique [16,34], k-edge connected components [35,36]. and k-plexes [63], have also been explored.…”

“…where v has the minimum clique-degree; 6 for each clique instance ψ containing v do 7 for each vertex u in ψ do 8 if deg G (u, Ψ)>deg G (v, Ψ) then 9 decrease u's clique-degree; 10 update G by removing v and its incident edges; 11 resort the vertices in V ; 12 return the array core[ ];…”

“…Proceedings of the VLDB Endowment, Vol. 12 in social piggybacking [30,31], which can be used to improve the throughput of social networking systems (e.g., Facebook). At present, two variants of DSD have been proposed.…”