The Model of Secure Social Networks Activity Based on Graph Theory

Abstract

The article deals with social networks parameters that describe individuals within network. The basic idea is based on an assumption that individuals with common characteristics are likely to communicate with each other. This is a kind of epidemical model with the chance of sending some information, as a functions of distance between source and potential destination. The main approach in the article is based on clustering of local characteristics of network. They characterize degree of interaction between the closest neighbors of current graph node. For the most networks if a node A is connected to node B and node B – to node C, then, there is a big chance of the fact, that node A is connected to node C (friends of our friends are also our friends). Depending on the graph structure, between two nodes there are often a few different paths. Distribution of nodes degree is a distribution with “long tail” and is modelled with degree distribution. It means, that in such networks, there are a lot of nodes, that has 1-3 neighbors, but a little of nodes, which has thousands of neighbors. A modelling of parameters (possible quantity of graph edges, clustering coefficient, connection of new node, shortest and average path, residual lifetime of chain, node interactions, average degree of node etc.) of social networks is taken. Calculations are illustrated with graphical materials. Relevant equations are represented.