A Complex Network Model Based on ´Friends of a Friend´ in a Fixed Community

In the real world, there are many complex networks with a fixed number of nodes, such as the friendship network in a class of a university. In this paper, we propose a "friends of a friend" based network (FFB network for short) model, in which the mechanism leading to a friendship connection between two persons is based on "friends of a friend": a person always try to strike up friendships with the friends of his friends. In the following experiment, we simulate the growing process of the FFB network and measure its average degree, degree distribution and clustering coefficient at different evolving stages. We also compare the FFB network with random network. The experiment results show that there are great differences between them in evolving process, degree distribution and clustering coefficient. Then, we give a mathematical expression of average degree in the FFB model and compare it with simulation results.