**No relation**

https://en.m.wikipedia.org/wiki/Degree_(graph_theory)

In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex’s degree, for the two ends of the edge

https://en.m.wikipedia.org/wiki/Vertex_(graph_theory)

n mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).

https://en.m.wikipedia.org/wiki/Cycle_(graph_theory)

n graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices.