A Distance Measure for Large Graphs based on Prime Graphs

Sofiane Lagraa (1) , Hamida Seba (2, 3) , Riadh Khennoufa (2) , Abir Mbaya (2) , Hamamache Kheddouci (2, 3)

1 LIG - Laboratoire d'Informatique de Grenoble
2 GrAMA - Graphes, Algorithmes et Multi-Agents
3 GOAL - Graphes, AlgOrithmes et AppLications

Graphs are universal modeling tools. They are used to represent objects and theirrelationships in almost all domains: they are used to represent DNA, images, videos, social networks,XML documents, etc.When objects are represented by graphs, the problem of their comparison is a problem of comparinggraphs. Comparing objects is a key task in our daily life. It is the core of a search engine, the backboneof a mining tool, etc. Nowadays,comparing objects faces the challenge of the large amount of data that this task must deal with.Moreover, when graphs are used to model these objects,it is known that graph comparison is very complex and computationally hard especially for largegraphs. So, research on simplifying graph comparison gained in interest and several solutions areproposed. In this paper, we explore and evaluate a new solution for the comparison of large graphs.Our approach relies on a compact encoding of graphs called prime graphs. These lasts are smaller andsimpler than the original ones but they retain the structure and properties of the encoded graphs. Wepropose to approximate the similarity between two graphs by comparing the corresponding primegraphs. Simulations results show that this approach is effective for large graphs.

Domaines: Informatique [cs]

Sofiane Lagraa, Hamida Seba, Riadh Khennoufa, Abir Mbaya, Hamamache Kheddouci. A Distance Measure for Large Graphs based on Prime Graphs. Pattern Recognition, 2014, 47, 2014, pp.2993-3005. ⟨10.1016/j.patcog.2014.03.014⟩. ⟨hal-01271721⟩