We investigate the connection structure in social network Live Journal (LJ) using main quantitative characteristics of its network such as the degree distribution, correlations, and clustering of secondary connections. These dependences are found to be scale invariant in a wide variety of values. The network is the assortative one. The shortest paths distribution between users has the sharp peak on six links. This confirms Milgram’s concept of six degrees of separation. Close location of most LJ-users along with its scale invariant structure allows treating it as small-world. In addition we study the resistance of LJ as environment of broadcast messages spreading with regard to targeted attacks and random failures.

small-worlds, social networks, scale invariance, power laws, vertex correlation, assortativity, the clustering of secondary connections, six degrees of separation, the resistance to targeted attacks and random failures.

Mathematical modelling in actual problems of science and technics