Definition:Loop-Graph/Incidence

Loop-Graph: Incidence

Although a loop is incident to only one vertex of a loop-graph, when measuring the degree of such a vertex, the loop is counted twice.

Thus, vertices $v_3$ and $v_4$ above have degree $5$, despite there being only four individual edges incident to those vertices.

Also see

• Results about loop-graphs can be found here.

Sources

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