Graph Theory

Graphs, \(G = (V, E) \) \(N \times N \) Adjacency Matrix \(N \times L \) Incidence Matrix \(A = \begin{bmatrix}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1\end{bmatrix} \) \(\hat{A} = \begin{bmatrix}1 & 0 & -1 & 0 \\ -1 & 1 & 0 & 0 \\ 0 & -1 & 1 & -1 \\ 0 & 0 & 0 & 1\end{bmatrix} \) \( V \) = set of \( N \) nodes\( E \) = set of \( L \) links \( A_{ij} = 1 \) iff \( (i, j) \in E \)Note that \(A\) need not be symmetric for directed graphs....