Networks become navigable as nodes move and forget

Abstract. We propose a dynamic process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable by a simple decentralized routing algorithm, known as greedy routing. Our model is based on the combination of two dynamics: a random walk (spatial) process, and an harmonic forgetting (temporal) process. Both processes reflect natural behaviors of the individuals, viewed as nodes in the network of inter-individual acquaintances. We prove that, in k-dimensional lattices, the combination of these two processes generates long-range links mutually independently distributed as a k-harmonic distribution. We analyze the performances of greedy routing at the stationary regime of our process, and prove that the expected number of steps for routing from any source to any target in any multidimensional lattice is a polylogarithmic function of the distan...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Augustin Chaintreau, Pierre Fraigniaud, Emmanuelle Lebhar
• Keywords: CORR 2008, Dynamic Process, Education, Network Evolution, Routing