There appears to be no standard term for a simpleconnected graph with exactly edges, though the words "polynema" (Kyrmse) and
"polyedge" (Muñiz 2011) have been proposed.
The numbers of -polynemas
for , 3 ... are 1, 1, 3, 5, 12, 30, 79,
227, ... (OEIS A002905).

An -polynema has nodes, where is its circuit rank.

Polynemas are related to a graphical construction problem called the match
problem (Gardner 1991).