Graphs
Definition: A graph is a collection of things (usually called vertices) together with a collection of pairs of vertices (called edges)
Note: Edges are NOT geometric => no specific shape, form length
Graphs can/do have many different visualization
A simple graph is the one without loops, without multiple edges.
The degree of a vertex, deg(v) = 2 x # of loops based at v + 1 x # of nonloop edges involving v
For an undirected graph, G, with n vertices, $ \sum_{i=0}^ndeg(v_i)=2E $
--Jniederh 00:08, 3 November 2008 (UTC)
Def: Given G with vertices v_1,...., v_k edges {e_ij)an edge between v_i and v_j, then the adjency matrix A is the square k X k matrix whose i-j-entry is # of edges from v_i to v_j
