Exploring Vertex-degree Sequences In Complex Networks And A Network Model Possessing Exponential Distribution

Since the Euler proposed the Seven Bridges of K?nigsberg problem, the study on graph has experienced three stages. They are regular network, random network and complex network respectively. The history of complex network is relatively short, meaning that complex network is a relatively new domain of science. Being different from traditional regular networks and random networks, complex network is more random than regular networks and is more regular than random networks. It exhibits some nontrivial network topological features. Though the history of complex is short, it has been a very popular domain among researchers. Especially, the study of complex networks is inspired largely by the research on computer networks and social networks.Generally, non-trivial topological features of complex networks include a short average path length, a high clustering coefficient, assortativity or disassortativity among vertices,b<Nl)(log where parameter b has certain rules that sometime it less than 2, and sometime it larger than 2,but it rarely larger than 3.The two much studied classes of complex networks are scale-free networks and small-world networks. Both have their own characteristics. A scale-free network is the network that vertex-degree distribution has power-law distributions. A small-world network is a network in which most nodes are not neighbours of one another, but most nodes can be reached from every other by a small number of hops or steps, exhibiting a feature that the world is small.The study on complex networks plays a more and more important role in real life, and the steps of the study continue to move forward. In addition to scale-free networks and small-world networks, it has appeared many other classes of complex networks possessing various characteristics. This article studies the vertex-degree sequences of complex networks and proposes a complex network with exponential distribution. It gives the definition of exponential distribution network and computes the various parameters of exponential distribution network. It also gives the the iterative algorithm for computer simulation for given value of parameters.Finally, it implements the algorithm using node JS language, displays the result graphically using cytoscape library, and verifies the parameters of complex networks.