Graphs in General

A generalized graph is a set of vertices and edges. We usually represent vertices as dots and the edges as lines connecting the dots. The edges, the lines, also called links, connect the vertices. A more formal definition is a graph, G, is a non-empty set of elements, the vertices, and a list of unordered pairs of these elements, the edges. The set of vertices of graph G is the vertex set of G; we denote this set by V(G), and the list of edges is the edge set of

G, denoted E(G). If v and w are vertices of G, then the edge vw connects or joins v and w.

Why graphs are so useful is that graph theory treats only the number of elements in a network and their relationships to each other, both in terms of the characteristics of the edge set. First some terms.

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