Solving a graph issue with Python

I have one situation and I would like to approach this problem with Python, but unfortunately I don't have enough knowledge about the graphs. I found one library which seems very suitable for this relatively simple task, networkx, but I am having issues doing exact things I want, which should be fairly simple.

I have a list of nodes, which can have different types, and two "classes" of neighbors, upwards and downwards. The task is to find paths between two target nodes, with some constraints in mind:

• only nodes of specific type can be traversed, i.e. if starting nodes are of type x, any node in the path has to be from another set of paths, y or z
• if a node has a type y, it can be passed through only once
• if a node has type z, it can be passed through twice
• in case a node of type z is visited, the exit has to be from the different class of neighbor, i.e. if its visited from upwards, the exit has to be from downwards

So, I tried some experimentation but I, as said, have struggled. First, I am unsure what type of graph this actually represents? Its not directional, since it doesn't matter if you go from node 1 to node 2, or from node 2 to node 1 (except in that last scenario, so that complicates things a bit...). This means I can't just create a graph which is simply multidirectional, since I have to have that constraint in mind. Second, I have to traverse through those nodes, but specify that only nodes of specific type have to be available for path. Also, in case the last scenario happens, I have to have in mind the entry and exit class/direction, which puts it in somewhat directed state.

Here is some sample mockup code:

import networkx as nx

G=nx.DiGraph()
G.add_node(1, type=1)
G.add_node(2, type=2)
G.add_node(3, type=3)
G.add_edge(1,2, side="up")
G.add_edge(1,3, side="up")
G.add_edge(2,1, side="down")
G.add_edge(2,3, side="down")
for path in nx.all_simple_paths(G,1,3):
    print path

The output is fairly nice, but I need these constraints. So, do you have some suggestions how can I implement these, or give me some more guidance regarding understanding this type of problem, or suggest a different approach or library for this problem? Maybe a simple dictionary based algorithm would fit this need?

Thanks!