The simplex geometry of graphs. (29th January 2019)

• Record Type: Journal Article
• Authors: Devriendt, Karel; Van Mieghem, Piet
• Editors: Estrada, Ernesto
• Is Part Of: Journal of complex networks. Volume 7:Number 4(2019)
• Page Start: 469
• Page End: 490
• Publication Date: 2019-01-29
• Subjects: Graph embedding -- Geometry of graphs -- Laplacian matrix -- Simplex geometry; Numerical analysis -- Periodicals; Computer networks -- Periodicals; Social networks -- Periodicals; 518.05
• DOI: 10.1093/comnet/cny036
• Languages: English
• ISSNs: 2051-1310

Abstract

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 unique way. 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.