Loop: An edge connecting a vertex to itself
Clique: A loop-free graph with every vertex connect to every other vertex
Vertices of attachment: For a subgraph H of a graph G, the v.o.a. are those vertices in H that have some incident edges in G not included in the subgraph H
Isthmus: An edge in a graph that has one of its ends of degree-1
Cutvertex: A vertex that its removal will make a connected graph/subgraph disconnected
Bridge: An edge that its removal will make a connected graph/subgraph disconnected
Cut: The set of edges that their removal will make a connected graph disconnected