Substance graphs are optimal simple-graph representations of metabolism

Substance graphs are optimal simple-graph representations of metabolism

One approach to studying the system-wide organization of biochemistry is to use statistical graph theory. Even in such a heavily simplified method, which disregards most of the dynamic aspects of biochemistry, one is faced with fundamental questions, such as how the chemical reaction systems should be reduced to a graph retaining as much functional information as possible from the original reac...

Model validation of simple-graph representations of metabolism.

The large-scale properties of chemical reaction systems, such as metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information, lists of chemical reactions, available in databases. Even for the simplest type of graph representation, this reduction can be done in several ways. We investigate different simple network representations by testing how well they ...

Clique graph representations of ptolemaic graphs

A graph is ptolemaic if and only if it is both chordal and distancehereditary. Thus, a ptolemaic graph G has two kinds of intersection graph representations: one from being chordal, and the other from being distance-hereditary. The first of these, called a clique tree representation, is easily generated from the clique graph of G (the intersection graph of the maximal complete subgraphs of G). ...

Width-Optimal Visibility Representations of Plane Graphs

Primal-Dual Representations of Planar Graphs and L-Contact Representations of Optimal 1-Planar Graphs

We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there exists a simultaneous representation of the graph and its dual with 3D boxes. We give a linear-time algorithm for constructing such a represen...