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Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees

In: Structural Analysis of Complex Networks

Author

Listed:
  • Alexander Mehler

    (Goethe-University Frankfurt am Main)

Abstract

This chapter introduces a novel class of graphs: Minimum Spanning Markovian Trees (MSMTs). The idea behind MSMTs is to provide spanning trees that minimize the costs of edge traversals in a Markovian manner, that is, in terms of the path starting with the root of the tree and ending at the vertex under consideration. In a second part, the chapter generalizes this class of spanning trees in order to allow for damped Markovian effects in the course of spanning. These two effects, (1) the sensitivity to the contexts generated by consecutive edges and (2) the decreasing impact of more antecedent (or “weakly remembered”) vertices, are well known in cognitive modeling [6, 10, 21, 23]. In this sense, the chapter can also be read as an effort to introduce a graph model to support the simulation of cognitive systems. Note that MSMTs are not to be confused with branching Markov chains or Markov trees [20] as we focus on generating spanning trees from given weighted undirected networks.

Suggested Citation

  • Alexander Mehler, 2011. "Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees," Springer Books, in: Matthias Dehmer (ed.), Structural Analysis of Complex Networks, chapter 0, pages 381-401, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4789-6_15
    DOI: 10.1007/978-0-8176-4789-6_15
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