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224 – Statistics as Support: Why Statistical Research on the Mental Health Conditions of United States Veterans Is a National Priority
Graph-theoretic Analysis of Complex Stochastic Networks
David H. Collins
Los Alamos National Laboratory
Aparna V. Huzurbazar
Los Alamos National Laboratory
We describe the use of graphs to represent Markovian and semi-Markovian stochastic networks, and how the interplay of visual and algebraic properties of the graphs aids in the determination of quantities such as first passage times. We also show how Markovian stochastic processes are special cases of generalized flowgraphs, with other special cases ranging from transportation networks to representations of finite automata. This leads to the formulation of general algorithms for graph reduction that can be expressed in terms of either visual or matrix-algebraic properties of the graph.