Spatial Graphs Cost and Efficiency: Exploring Edges Competition by MCMC
Recent models for spatial networks have been built by determining graphs minimizing some functional F composed by two antagonist quantities. Although these quantities might differ from a model to another, methods used to solve these problems generally make use of simulated annealing or operations research methods, limiting themselves to the study of a single minimum and ignoring other close-to-optimal alternatives. This contribution considers the arguably promising framework where the functional F is composed by a graph cost and a graph efficiency, and the space of all possible graphs on n spatially fixed nodes is explored by MCMC. Covariance between edges occupancy can be derived from this exploration, revealing the presence of cooperative and competition regimes, further enlightening the nature of the alternatives to the locally optimal solution.
KeywordsMonte Carlo Markov Chain Spatial Network Cooling Schedule Graph History Airline Network
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