An evolutionary model for the origin of modularity in a complex gene network

Scale-free cellular networks are organized into a complex topology by massive interactions (links) between nodes, which can be typically characterized by a power-law degree. In contrast, almost all cellular networks show the feature of modularity. The popular BA model (Barabasi and Albert) demonstrated the origin of scale-free property by the attachment preference, but not for the origin of modularity. We propose a BBA model (Biological BA) by introducing the random link-loss mechanism under the original BA model, showing that scale-free and modularity can emerge as a derived property of the BBA model. Data analysis has shown that, roughly, the rate of gene network evolution can be described as a 2-2-1 pattern (adding two new genes and two new links with the cost of one link-loss).