A NOVEL SMALL-WORLD NETWORK MODEL: KEEPING CONNECTIVITY WITHOUT ADDING EDGES

Abstract

Considering the problems of potentially generating a disconnected network in the WS small-world network model [Watts and Strogatz, Nature393, 440 (1998)] and of adding edges in the NW small-world network model [Newman and Watts, Phys. Lett. A263, 341 (1999)], we propose a novel small-world network model. First, generate a regular ring lattice of N vertices. Second, randomly rewire each edge of the lattice with probability p. During the random rewiring procedure, keep the edges between the two nearest neighbor vertices, namely, always keep a connected ring. This model need not add edges and can maintain connectivity of the network at all times in the random rewiring procedure. Simulation results show that the novel model has the typical small-world properties which are small characteristic path length and high clustering coefficient. For large N, the model is approximately equal to the WS model. For large N and small p, the model is approximately equal to the WS model or the NW model.