Investigation of the Optimized Network Properties

An-Liang Cheng^1*, Pik-Yin Lai^1,2

¹Department of Physics, National Central University, Taoyuan City, Taiwan
²Center for complex system, National Central University, Taoyuan City, Taiwan

* Presenter:An-Liang Cheng, email:phairst@gmail.com

We consider network growing models that aim at minimizing the wiring cost while at the same time maximizing the important network properties such as the network connections. By mapping the system to an Ising spin model, we obtain analytic results for two such models, both of them show interesting, but different phase transition behaviors for general wiring cost distributions, and node weight distributions. Depending on the properties of the edge and node weights distributions, the system can exhibit a variety of phase transitions, including first-order, second-order and hybrid ones, from no connection to a network of finite fraction of connections. We use the mean-field theory to propose an effective algorithm for finding the fully optimized (zero-temperature) network configurations that is orders of magnitude faster than using simulated annealing to low temperatures. Furthermore, we analytically derive some optimized network properties, including the clustering coefficient, average path length, small-world-ness, degree distribution and weight distribution. The scaling properties of the optimized network are also discussed.

Keywords: Optimized networks, Phase transition, Mean-field theory, Small-world-ness, Degree distribution