Summarizing and Understanding Large Graphs
with Danai Koutra, U Kang, and Christos Faloutsos

Abstract. How can we succinctly describe a million-node graph with a few simple sentences? How can we measure the importance' of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a vocabulary' of subgraph-types that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a well-founded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph.

Our contributions are three-fold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop VoG, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multi-million-edge real graphs, including Flickr and the Notre Dame web graph.

## Implementation

the Matlab/Python source code (v1.2, September 2014), by Danai Koutra, Jilles Vreeken & U Kang.

## Related Publications

 Koutra, D, Kang, U, Vreeken, J & Faloutsos, C Summarizing and Understanding Large Graphs. Statistical Analysis and Data Mining vol.8(3), pp 183-202, Wiley, 2015. Koutra, D, Kang, U, Vreeken, J & Faloutsos, C VoG: Summarizing and Understanding Large Graphs. In: Proceedings of the SIAM International Conference on Data Mining (SDM), pp 91-99, SIAM, 2014.