Nihonbashi 1-chome Mitsui Building, 15th floor, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
Dr. Tiphaine Viard (National Conservatory of Arts and Techniques, France)
Stream graphs and link streams for the modelisation of interactions over time, and application to event detection in IP traffic
Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a dedicated formalism. In this talk, we present a generalization of graph concepts in order to cope with both aspects in a consistent way. We start with elementary concepts like density, clusters, or paths, and derive from them more advanced concepts like cliques, degrees, clustering coefficients, or connected components. We obtain a language to directly deal with interactions over time, similar to the language provided by graphs to deal with relations. This formalism is self-consistent: usual relations between different concepts are preserved. It is also consistent with graph theory: graph concepts are special cases of the ones we introduce. This makes it easy to generalize higher-level objects such as quotient graphs, line graphs, k-cores, and centralities. We will present some applications of this formalism, in particular the analysis of IP traffic and event detection in such traffic.
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