If e = {u,v} then HasEdge(G,e) returns true if the undirected graph G contains the (undirected) edge {u,v}, and false otherwise.

If a = [u,v], a directed edge, HasEdge(G,a) returns true if the undirected graph G has the undirected edge {u,v} in it.

If a = [u,v], HasArc(G,a) returns true if the directed graph G has the directed edge from vertex u to v in it, and false otherwise.

If e = {u,v}, HasArc(G,a) returns true if the directed graph G has both edges [u,v] and [v,u] in it, and false otherwise.

Because the data structure for a graph is an array of sets of neighbors, the test for edge membership uses binary search and hence the cost is O(log k) where k is the number of neighbors.