A multi-community homogeneous small-world network and its fundamental characteristics

• We propose a new concept to generate a small-world network having community structure.
• A generating algorithm is presented and its network parameters are explored.
• We discuss the fundamental characteristics of the proposed topology by using a spatial prisoner’s dilemma game as template.

We introduce a new small-world network–which we call the multi-community homogeneous-small-world network–that is divided into multiple communities that are relatively isolated, similar to sparsely connected islands. A generating algorithm is presented and its network parameters are explored. To elucidate the fundamental characteristics of the proposed topology, we adopt spatial prisoner’s dilemma games as a template for discussion. Comparing with a conventional homogeneous small-world network, more enhanced network reciprocity is observed in games where a stag hunt-type dilemma is large. With intensive analysis, we find how this enhancement is brought about.