Abstract
Simulations are often used in the study of metro network systems and the interactions of passengers with such systems in the real life. Graph theory is used to represent such metro systems. Simple random graphs are generated using a random graph generation algorithm revolving around random walks. The goal is to use such graphs to analyze the effects of the topologies of the graph parallel to the events which happen in real metro systems. This is done through random walks on the graphs by Monte Carlo Simulation of those random walkers. The simulations showed that the degree of a node in the graph has a near linear relationship with the number of times a specific node has been visited.
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