  We focus on the heterogeneity of social networks and its role to the
emergence of prevailing cooperation and sustaining cooperators. The social
networks are representative of the interaction relationships between players
and their encounters in each round of games. We study an evolutionary
Prisoner's Dilemma game on a variant of Watts-Strogatz small-world network,
whose heterogeneity can be tuned by a parameter. It is found that optimal
cooperation level exists at some intermediate topological heterogeneity for
different temptations to defect. Moreover, neither the most heterogeneous case
nor the most homogeneous one would favor the cooperators. At intermediate
heterogeneity in degree sequences, cooperators could resist the invasion of
defectors for large temptation to defect.
