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

Abstract

Abstract-Given a real world graph, how should we layout its edges? How can we compress it? These questions are closely related, and the typical approach so far is to find cliquelike 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 SLASHBURN 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 SLASHBURN method consistently outperforms other methods on all datasets, giving good compression and faster running time.

Node Re-Ordering as a Means of Anomaly Detection in Time-Evolving Graphs

“…Random permutation serves as a naive baseline; RCM is a classical bandwidth reduction algorithm [6]; and SlashBurn is a recent method that is shown to produce adjacency matrices with localized non-zero elements. This method is shown to be one of the best state-of-the-art methods [14].…”

“…Experiment IV: Amplay Stability We compare Amplay with other ordering methods, namely random, RCM [6], and SlashBurn [14]. Random permutation serves as a naive baseline; RCM is a classical bandwidth reduction algorithm [6]; and SlashBurn is a recent method that is shown to produce adjacency matrices with localized non-zero elements.…”

“…Moreover, we designed experiments for the purpose of anomaly Fig. 8: Amplay stability in comparison to the rival approaches, SlashBurn [14], RCM [6] and Random ordering, as we vary the percentage of vertices with low degree that we ignored.…”

Clearing Contamination in Large Networks

“…However, as most real world social networks exhibit a power-law degree distribution we know that the hub nodes will often be required in the FVS. This idea was utilized in [16] to find communities in real world networks and we take a similar approach when considering social networks. In [16] the k-hubset is defined as the set of nodes with the top k highest degrees.…”

“…This idea was utilized in [16] to find communities in real world networks and we take a similar approach when considering social networks. In [16] the k-hubset is defined as the set of nodes with the top k highest degrees. For our optimization, we compute the k-hubset of G and take its union with the computed FVS to arrive at the set of permanent guards to be used for the sliding FVS.…”