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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _theorem5p4(adj, ub):
 """By Theorem 5.4, if any two vertices have ub + 1 common neighbors then we can add an edge between them. """

    new_edges = set()
    for u, v in itertools.combinations(adj, 2):
        if u in adj[v]:
            # already an edge
            continue

        if len(adj[u].intersection(adj[v])) > ub:
            new_edges.add((u, v))

    while new_edges:
        for u, v in new_edges:
            adj[u].add(v)
            adj[v].add(u)

        new_edges = set()
        for u, v in itertools.combinations(adj, 2):
            if u in adj[v]:
                continue

            if len(adj[u].intersection(adj[v])) > ub:
                new_edges.add((u, v))