On the Emergence of Shortest Paths by Reinforced Random Walks
This addresses a fundamental problem in network science for researchers studying decentralized navigation and adaptive systems, though it appears incremental as it builds on existing biased random walk models.
The paper tackles the co-evolution of network structure and navigation efficiency by proposing a model where edge weights adjust based on traversed path lengths, proving that biased random walks eventually converge to shortest paths with non-shortest path probabilities decaying as a power-law.
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate the interplay between the efficiency of network navigation (i.e., path lengths) and network structure (i.e., edge weights). We propose a simple and tractable model based on iterative biased random walks where edge weights increase over time as function of the traversed path length. Under mild assumptions, we prove that biased random walks will eventually only traverse shortest paths in their journey towards the destination. We further characterize the transient regime proving that the probability to traverse non-shortest paths decays according to a power-law. We also highlight various properties in this dynamic, such as the trade-off between exploration and convergence, and preservation of initial network plasticity. We believe the proposed model and results can be of interest to various domains where biased random walks and decentralized navigation have been applied.