Final Code

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
@author: ahnaqvi
"""

# take grant rules to check for info sharing


def create(subject, created_entity_type, rights_of_subject_over_created_entity, initial_graph):# rights of sub over created is a string
    created_entity_type.append(len(initial_graph[0])+1)
    initial_graph[subject].append(rights_of_subject_over_created_entity)
    for i in graph.keys():
        if i != subject:
            graph[i].append("")




def tg_connected(nodeA, nodeB, graph):
    visited = [False]*len(graph.keys())
    queue = []
    queue.append(nodeA)
    visited[nodeA] = True
    while queue:
        n = queue.pop()
        if n == nodeB:
            return True
        for i,x in enumerate(graph[n]):
            print(i,x)
            if 't' in x or 'g' in x:
                if visited[i] == False:
                    queue.append(i)
                    visited[i] = True
    return False

def can_share(graph, right, x, p, subjects): # x and p are nodes. right is a character for eg. 'x' or 'w'
    if p not in subjects:
        return False
    if right in graph[p][x] or graph[x][p]:
        return True
    for subject in subjects:
        if right in graph[subject][x]:
            if tg_connected(subject,p) or tg_connected(p,subject):
                return True
    return False

def remove(right, s, x, graph, subjects):
    if s in subjects:
        if right in graph[s][x]:
            new_rights = graph[s][x]
            new_rights = new_rights.replace(right, "")
            graph[s][x] = new_rights

# an example graph is given at the top. The function can_share checks if sharing  is allowed between two nodes or not. One can use to check if a system is safe or not with regards to a given access profile, for eg a company policy. This system does not deal with theft of rights/flow.


graph = dict()

users = [0,1,2]
files = [3,4,5]

# define initial graph
graph[0] = ["","r","","rwx","",""]
graph[1] = ["","","","","",""]
graph[2] = ["","","","","t","r"]
graph[3] = ["","","","","",""]
graph[4] = ["","g","","","",""]
graph[5] = ["","","","","",""]

print(can_share(graph, "r", 1, 4, users)) # should return False
print(can_share(graph, "r", 1, 0, users)) # should print True


#################################################################
# Addendum: The original report stated that Dijkstras and Floyd's algorithm were used. Dijstra's can be used here to find the shortest path to share info. However, it is not needed to KNOW if sharing can happen between two nodes, which is what we're after.