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This will be faster to compute all intervals at once.

def intervals(g):
    import itertools
    dist = g.distance_all_pairs()
    intervals = dict()
    for u,v in itertools.combinations(g.vertices(), 2):
        intervals[u,v] = list()
        for w in g.vertices():
            if u!=w and v!=w and dist[u][v]==dist[u][w]+dist[w][v]:
                intervals[u,v].append(w)
        intervals[v,u] = copy(intervals[u,v])
    return intervals