The simplex geometry of graphs

Karel Devriendt, Piet Van Mieghem

Research output: Contribution to journalReview articlepeer-review

8 Citations (Scopus)
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Abstract

Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods, each of which highlights the properties of graphs in a uniqueway. Here, we discuss a novel approach to study graphs: the simplex geometry (a simplex is a generalized triangle). This perspective, proposed by Miroslav Fiedler, introduces techniques from (simplex) geometry into the field of graph theory and conversely, via an exact correspondence. We introduce this graph-simplex correspondence, identify a number of basic connections between graph characteristics and simplex properties, and suggest some applications as example.
Original languageEnglish
Pages (from-to)469-490
Number of pages22
JournalJournal of Complex Networks
Volume7
Issue number4
DOIs
Publication statusPublished - Aug 2019

Keywords

  • Graph embedding
  • Geometry of graphs
  • Laplacian matrix
  • Simplex geometry

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