Spawning Nodes Generate Deterministic Scale-Free Networks

Abstract

In this paper we present a deterministic vertex spawning model that yields a scale-free network. The model specifies that a parent vertex produces a child vertex in a time interval approximately proportional to the current time and inversely proportional to the number of edges currently connected to the parent. Spawned offspring maintain an undirected edge with its parent. No information about the network as a whole is required to obtain scale-invariant behavior. Although the algorithm is deterministic, the number of nodes spawning in a small time interval quickly becomes randomized. We show theoretically and with simulations that such a spawned network will have a degree distribution obeying a power law with exponent 2.5. Simulations show that the distribution matches a Zipf distribution.