Study on an evolving complex network with fixed number of vertices

The purpose of this paper is to propose a complex network model which can study the specified objects in a complex system within which the number of agents is fixed while the interactions and the outside environments are evolving with time.

The complex network model is analyzed by the master equation method and the rigorous four‐step statistical test is applied to test whether the degree distribution in the real world fits power law or not.

By theoretical analysis, the vertex degrees of the model follow power law distribution p(k)∼k⁻² which is different from that of the Barabási‐Albert model. By empirical research, the result shows that the citations of papers published in 2001 on the small‐world networks follow a power law distribution which is tested by the statistical test.

The small sample and short evolving time may cause some deviation from the theoretical expectation.

This evolving complex network model with fixed number of vertices and the statistical test process for power‐law will have a great significance for the theoretical and empirical study on complex networks.

This paper presents a new model of evolving complex networks which can be used to analyze the specified objects in a dynamic system and a quantitative method for power law test.