# Find the probability of occurrence of each edge in a graph having \$n\$ nodes after \$k\$ operations

Given a graph with $$n$$ nodes . The adjacency matrix of the graph is given. We do $$k$$ operations on this graph. In each operation we choose two distinct nodes $$i$$ and $$j$$ (there are $$(n*(n-1))/2$$ such choices) equiprobably (all choices are equiprobable) and if there exists a edge between $$i$$ and $$j$$ we delete that edge or else we draw an edge between the chosen pair of nodes.
We have to output a $$n*n$$ matrix where the element at $$(i,j)th$$ position denotes the probability of occurrence of edge connecting the nodes $$i$$ and $$j$$ in the final resulting graph.
The constraints on n and k are $$n<=50$$ and $$k<=50$$ .
I tried it using dynamic programming but could figure out transitions properly.