A new matrix representation of multidigraphs

Figures & data

Fig. 1 A multidigraph $G$ on $7$ vertices.

Fig. 2 A multidigraph $G$, its underlying undirected simple graph $G_{\mathrm{u}}$ and associated weighted directed graph $G_{\mathrm{w}}$.

Fig. 3 A non-bipartite multidigraph $G$ whose $A_{ℂ}$-spectrum is symmetric about origin and $G_{\mathrm{w}}$, the corresponding associated weighted cycle digraph.

Fig. 4 The associated weighted digraph of a type-$2$ bipartite multidigraph $K_{p,q}^r(w,m)$.

Fig. 5 The associated weighted digraphs of a double star multidigraph and a pendant-merge double star multidigraph.

Fig. 6 Example of a multidigraph $G$, its weighted digraph $G_{\mathrm{w}}$ and corresponding modular graph $\left|G\right|$.