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Structural Analysis of Complex Networks pp 381–401Cite as

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

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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.

MSC2000: Primary 05C05, 68R10; Secondary 05C12, 05C38, 05C75

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Acknowledgments

Financial support of the German Federal Ministry of Education (BMBF) through the research project Linguistic Networks and of the German Research Foundation (DFG) through the Excellence Cluster 277 Cognitive Interaction Technology (via the Project Knowledge Enhanced Embodied Cognitive Interaction Technologies (KnowCIT)), the SFB 673 Alignment in Communication (via the Project X1 Multimodal Alignment Corpora: Statistical Modeling and Information Management), the Research Group 437 Text Technological Information Modeling (via the Project A4 Induction of Document Grammars for Webgenre Representation), and the LIS-Project Content-Based P2P-Agents for Thematic Structuring and Search Optimization in Digital Libraries at Bielefeld University is gratefully acknowledged.

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  1. Goethe-University Frankfurt am Main, Senckenberganlage 31, 60325, Frankfurt am Main, Germany

    Alexander Mehler

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  1. Alexander Mehler
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Correspondence to Alexander Mehler .

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  1. Medizinische Informatik und Technik, Institute for Bioinformatics and Transla, UMIT-Private Universität für Gesundheits, Eduard Wallnöfer-Zentrum 1, Hall in Tirol, A-6060, Austria

    Matthias Dehmer

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Mehler, A. (2011). Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees. In: Dehmer, M. (eds) Structural Analysis of Complex Networks. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4789-6_15

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