By Shi M., Yuan X., Cai M.

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Additional resources for (3,k)-Factor-Critical Graphs and Toughness

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The synopsis construction is typically defined through either node or edge contractions. The key is to define a synopsis which retains the relevant structural property of the underlying graph. In [7], the algorithm in [177] is used in order to collapse the dense regions of the graph, and represent the summarized graph in terms of sparse regions. The resulting contracted graph still retains important structural properties such as the connectivity of the graph. In [46], a randomized summarization technique is used in order to determine frequent patterns in the underlying graph.

This summarization is then leveraged in order to determine the frequent subgraph patterns from the data. Bounds are derived in [46] on the false positives and false negatives with the use of such an approach. Another challenging variation is when the frequent patterns are overlaid on a very large graph, as a result of which patterns may themselves be very large subgraphs. An algorithm called TSMiner was proposed in [110] to determine frequent structures in very large scale graphs. Graph pattern mining has numerous applications for a variety of applications.

Matsumoto. An Application of Boosting to Graph Classification, NIPS Conf. 2004. [19] J. Leskovec, J. Kleinberg, C. Faloutsos. Graph Evolution: Densification and Shrinking Diameters. ACM Transactions on Knowledge Discovery from Data (ACM TKDD), 1(1), 2007. [20] K. Liu and E. Terzi. Towards identity anonymization on graphs. ACM SIGMOD Conference 2008. [21] R. Kumar, P Raghavan, S. Rajagopalan, D. Sivakumar, A. Tomkins, E. Upfal. The Web as a Graph. ACM PODS Conference, 2000. An Introduction to Graph Data 11 [22] S.

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