Assuming an adjacency list as data structure of a directed Graph, it is not completely clear to me how "contraction of an edge" is defined.
Let me cite the definition I do have at hand:
Source: JAMES B. ORLIN - A FASTER STRONGLY POLYNOMIAL MINIMUM COST FLOW ALGORITHM, Section 4.1. Contraction
[...] any edge, say $(k, \ell)$, can be contracted into a single node $p$. The contraction operation consists of: letting $b(p) = b(k) + b(\ell)$ and $e(p) = e(k) + e(\ell)$; replacing each edge $(i, k)$ or $(i, \ell)$ by the edge $(i, p)$; replacing each edge $(k, i)$ or $(\ell, i)$ by the edge $(p, i)$; and letting the cost of an edge in the contracted network equal that of the edge it replaces.[...]
$b$ and $p$ are functions defining values for certain properties of a node; their meaning is unimportant for understanding contraction.
Consider the following graph described in "adjacency speak", where e.g. node 0 has an edge to the nodes 1, 2 and 5; node 5 has no outgoing edges; node 3 has an edge to node 4 and so on...
0 -> 1, 2, 5 1 -> 2, 3 2 -> 1 3 -> 4 4 -> 5 5
Now I want to contract the edge $(1,2)$. Note that there is an edge $(2,1)$, too. Should the application of the contraction operation yield the following directed graph, where the newly introduced node $p$ has the id $6$?
0 -> 6, 5 3 -> 4 4 -> 5 5 6 -> 3, 3, 5, 6 # Note that we got two edges from node 6 to node 3. # Note that we also have an edge from 6 to 6, i.e. a loop.
Thanks a lot!