graph representations

Three different ways to store the same graph in a computer: a list of each vertex's neighbors, a matrix of who's adjacent to whom, or a matrix of which vertex touches which edge.

An adjacency list stores, per vertex, the list of its neighbors. An adjacency matrix is a $|V|\times|V|$ matrix $A$ with $A_{ij}=1$ iff vertices $i,j$ are adjacent. An incidence matrix is a $|V|\times|E|$ matrix with a $1$ in row $v$ , column $e$ iff $v$ is an endpoint of $e$ .