Symmetric Relation - Graph-theoretic Interpretation

Graph-theoretic Interpretation

In an undirected graph, the relation over the set of vertices of the graph under which v and w are related if and only if they are adjacent forms a symmetric relation. Conversely, if R is a symmetric relation over a set X, one can interpret it as describing an undirected graph with the elements of X as the vertices and the pairs in R as the edges. Thus, symmetric relations and undirected graphs are combinatorially equivalent objects.