Summation of all links that contains nieghbors to certain node in Graph

Question

I'm trying to model a constraint in Python using Pulp and networkX that is getting the sum of the edges that contain this node over all the nodes. The constraint can be like that: $$\sum_{m\in\cal N}z_{(m,n)}\succeq k(1-y_m),\quad\forall m\in\cal N.$$

I have used this code to model the constraint:

for m in g.nodes(): prob += pulp.lpSum(z[(m,n)] for m in g.nodes()) >= k*(1-y[m])

This piece of code rises an error about the key of the dictionary since the variable dictionary $z$ doesn't contains all the neighbors values. If I used this instead

for m in g.nodes(): prob += pulp.lpSum(z[(m,n)] for (u,v) in g.edges()) >= k*(1-y[m])

It sums all the links, not the ones associated with link $m$.

I would like your help with this!.

Please be noted that $z_{(m,n)}$ is a dict of the graph edges

Answer 1

Alternatively, just like in your previous question :

for m in g.nodes():
    prob += pulp.lpSum(z[(m,n)] for n in g.neighbors(m)) >= k*(1-y[m])

Answer 2

You can use:

all_neighbors(graph, node): Returns all of the neighbors of a node in the graph.

function in networkX to find all the nodes which are connected to node m and then use the first constraint that you mentioned. I think there is a typo in the constraint as well instead of $m$ you should have $n$ (it's confusing). The output of that function is iterator you need to save it as a list (I am not sure about the format that PuLP accept).