This compositional data analysis theory and applications pdf is about sets of vertices connected by edges. For graphs of mathematical functions, see Graph of a function. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

A graph in this context is made up of vertices, nodes, or points which are connected by edges, arcs, or lines. Graphs are one of the prime objects of study in discrete mathematics. Refer to the glossary of graph theory for basic definitions in graph theory. Definitions in graph theory vary.

The following are some of the more basic ways of defining graphs and related mathematical structures. To avoid ambiguity, this type of graph may be described precisely as undirected and simple. Other senses of graph stem from different conceptions of the edge set.

In one more generalized notion, V is a set together with a relation of incidence that associates with each edge two vertices. Many authors call this type of object a multigraph or pseudograph. All of these variants and others are described more fully below.