FURS: Fast and Unique Representative Subset selection retaining large-scale community structure

We propose a novel algorithm, FURS (Fast and Unique Representative Subset selection) to deterministically select a set of nodes from a given graph which retains the underlying community structure. FURS greedily selects nodes with high-degree centrality from most or all the communities in the network. The nodes with high-degree centrality for each community are usually located at the center rather than the periphery and can better capture the community structure. The nodes are selected such that they are not isolated but can form disconnected components. The FURS is evaluated by quality measures, such as coverage, clustering coefficients, degree distributions and variation of information. Empirically, we observe that the nodes are selected such that most or all of the communities in the original network are retained. We compare our proposed technique with state-of-the-art methods like SlashBurn, Forest-Fire, Metropolis and Snowball Expansion sampling techniques. We evaluate FURS on several synthetic and real-world networks of varying size to demonstrate the high quality of our subset while preserving the community structure. The subset generated by the FURS method can be effectively utilized by model-based approaches with out-of-sample extension properties for inferring community affiliation of the large-scale networks. A consequence of FURS is that the selected subset is also a good candidate set for simple diffusion model. We compare the spread of information over time using FURS for several real-world networks with random node selection, hubs selection, spokes selection, high eigenvector centrality, high Pagerank, high betweenness centrality and low betweenness centrality-based representative subset selection.