Network with Positive Integer Mapping is Multigraph/Examples/Arbitrary Order 3 Network

Example of Use of Network with Positive Integer Mapping is Multigraph

Let $G = \struct {V, E}$ be the undirected graph defined as:

$V = \set {v_1, v_2, v_3}$

$E = \set {v_1 v_2, v_1 v_3, v_2 v_3}$

Let $w: E \to \R$ be the weight function defined as:

$w = \set {\tuple {v_1 v_2, 2}, \tuple {v_1 v_3, 1}, \tuple {v_2 v_3, 3} }$

Then the undirected network $\struct {G, w}$ can be represented diagrammatically in either of the forms shown below:

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.6$: Networks as Mathematical Models