Beyond 'Caveman Communities': Hubs and Spokes for Graph Compression and Mining

Abstract

Given a real world graph, how should we lay-out its edges? How can we compress it? These questions are closely related, and the typical approach so far is to find clique-like communities, like the `cavemen graph', and compress them. We show that the block-diagonal mental image of the `cavemen graph' is the wrong paradigm, in full agreement with earlier results that real world graphs have no good cuts. Instead, we propose to envision graphs as a collection of hubs connecting spokes, with super-hubs connecting the hubs, and so on, recursively. Based on the idea, we propose the Slash Burn method (burn the hubs, and slash the remaining graph into smaller connected components). Our view point has several advantages: (a) it avoids the `no good cuts' problem, (b) it gives better compression, and (c) it leads to faster execution times for matrix-vector operations, which are the back-bone of most graph processing tools. Experimental results show that our Slash Burn method consistently outperforms other methods on all datasets, giving good compression and faster running time.