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Large-scale analysis of structural branching measures

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Abstract

Structural branching of graphs has been investigated extensively. Yet, no method/model has yet been developed which captures all aspects of branching meaningfully. Another shortcoming of nearly all related work in this area is the fact that only small sets of example graphs have been used to perform those studies. Instead, we investigate structural branching of graphs statistically by using large sets of exhaustively generated graphs. Our findings explain some of the limits of existing branching measures as well as the search for novel branching measures by using correlation analysis.

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Notes

  1. The star graph is the tree of order \(N\) with \(N-1\) vertices of degree \(1\). The path graph is the tree of order \(N\) without vertices of a degree greater than \(2\).

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Acknowledgments

Matthias Dehmer thanks the Austrian Science Funds (project P22029-N13) and the Standortagentur Tirol for supporting this work.

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  1. Institute for Bioinformatics and Translational Research, UMIT, Hall in Tirol, Austria

    Michael Schutte & Matthias Dehmer

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  1. Michael Schutte
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  2. Matthias Dehmer
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Correspondence to Matthias Dehmer.

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Schutte, M., Dehmer, M. Large-scale analysis of structural branching measures. J Math Chem 52, 805–819 (2014). https://doi.org/10.1007/s10910-013-0294-9

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