Abstract

We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a divergent correlation length as the degree of randomness tends to zero. We propose a real-space renormalization group transformation for the model and demonstrate that the transformation is exact in the limit of large system size. We use this result to calculate the exact value of the single critical exponent for the system, and to derive the scaling form for the average number of \degrees of separation" between two nodes on the network as a function of the three independent variables. We conrm our results by extensive numerical simulation. 1 I. INTRODUCTION Folk wisdom holds that there are \six degrees of separation" between any two human beings on the planet|i.e., a path of no more than six acquaintances linking any person to any other....

Citations