Stochastic networks Auteur(s): Basileu C., Ben amor Soufian, Bui Marc, Bounekkar A., Kabachi N., Lamure M.
Conference: 10ème journées Francophones "Extraction et Gestion des Connaissances" (EGC 2010) (Hammamet, TN, 2010-01-26) Résumé: Social sciences widely use the concept of network for modeling links between individuals. (Social networks) A lot of works have been proposed on different problems related to this concept. For example, what percentage of nodes of the network is required to observe a si- gnificant change in the connectivity of the network ? Or, what are nodes the most linked to others ? The common point of these Works is that they all model a social network by a graph, in the mathematical sense. However, we think a social network is composed from different types of links between individuals, which implies using more than one graph. So we propose a new formalism for modeling social networks, based on families of graphs. This formalism enables to study topological properties of a network by means of a weakened version of mathematical topology (pretopology). As a second point, we assume that links between individuals cannot be considered as certain and that many events can influence existence of these links. In most cases, these events are not predictable, so we introduce stochastic aspects in modeling a network. This leads us to the concept of stochastic network. In this paper, we first give basic definitions of a network, of a stochastic network and some elements about underlying mathematical theories : pretopologie and random sets. Then, we give first results about modeling the topology of a stochastic network, with some particu- lar points concerning transmission and connectivity. We conclude with perspectives of further works. |