Graphs and Degrees · Medium problem

A technician logs every cable she tests between two of six servers, as the pairs $(1,2),(2,1),(1,3),(3,4),(4,3),(2,3),(1,2),(5,6),(6,5),(1,4),(2,5),(3,5),(1,3),(4,5),(2,4),(3,6),(6,1),(1,6),(5,2),(4,6)$ — $20$ entries in all, since she sometimes logs the same cable from either end or re-tests one. Treating each cable as an edge $\{u,v\}$ of a graph, how many DISTINCT cables does the log actually describe?