Merging Module Model for a Network with Scale-Free Properties and Modularity

Many graphical and statistical properties have been found in a large size of complex networks such as WWW, social and biomolecular networks [1, 3]. One of the common properties is scale-free, shows that the degree distribution P (k) of the networks follows power law P (k) ∼ k . Recent study demonstrates that metabolic networks in different organisms also have both modularity and hierarchy [5]. To get an insight into their origin and growing mechanisms of the networks, here we present a simple model that consists of deterministic and stochastic process.