Asymmetry between odd and even node weight in complex networks

Phenomenon of asymmetry between odd and even node weight distribution in some complex networks, such as public transportation networks and Internet, is presented. Reasons related to this phenomenon are summarized, i.e., (1) edges are solid connections between nodes which are embedded in real geometric background, and (2) preferential mechanism during the process of network formation. Incorporating these two points, complex networks are constructed by self-avoiding random walk on 2D grid and the simulation results are consistent well with that of empirical researches.