simrank_similarity¶

simrank_similarity(G, source=None, target=None, importance_factor=0.9, max_iterations=1000, tolerance=0.0001)[source]¶

Returns the SimRank similarity of nodes in the graph G.

SimRank is a similarity metric that says “two objects are considered to be similar if they are referenced by similar objects.” [1].

The pseudo-code definition from the paper is:

def simrank(G, u, v):
    in_neighbors_u = G.predecessors(u)
    in_neighbors_v = G.predecessors(v)
    scale = C / (len(in_neighbors_u) * len(in_neighbors_v))
    return scale * sum(simrank(G, w, x)
                       for w, x in product(in_neighbors_u,
                                           in_neighbors_v))

where G is the graph, u is the source, v is the target, and C is a float decay or importance factor between 0 and 1.

The SimRank algorithm for determining node similarity is defined in [2].

Parameters

GNetworkX graph: A NetworkX graph
sourcenode: If this is specified, the returned dictionary maps each node v in the graph to the similarity between source and v.
targetnode: If both source and target are specified, the similarity value between source and target is returned. If target is specified but source is not, this argument is ignored.
importance_factorfloat: The relative importance of indirect neighbors with respect to direct neighbors.
max_iterationsinteger: Maximum number of iterations.
tolerancefloat: Error tolerance used to check convergence. When an iteration of the algorithm finds that no similarity value changes more than this amount, the algorithm halts.

Returns

similaritydictionary or float

If source and target are both None, this returns a dictionary of dictionaries, where keys are node pairs and value are similarity of the pair of nodes.

If source is not None but target is, this returns a dictionary mapping node to the similarity of source and that node.

If neither source nor target is None, this returns the similarity value for the given pair of nodes.

References

1: https://en.wikipedia.org/wiki/SimRank
2: G. Jeh and J. Widom. “SimRank: a measure of structural-context similarity”, In KDD’02: Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 538–543. ACM Press, 2002.

Examples

>>> G = nx.cycle_graph(2)
>>> nx.simrank_similarity(G)
{0: {0: 1.0, 1: 0.0}, 1: {0: 0.0, 1: 1.0}}
>>> nx.simrank_similarity(G, source=0)
{0: 1.0, 1: 0.0}
>>> nx.simrank_similarity(G, source=0, target=0)
1.0

The result of this function can be converted to a numpy array representing the SimRank matrix by using the node order of the graph to determine which row and column represent each node. Other ordering of nodes is also possible.

>>> import numpy as np
>>> sim = nx.simrank_similarity(G)
>>> np.array([[sim[u][v] for v in G] for u in G])
array([[1., 0.],
       [0., 1.]])
>>> sim_1d = nx.simrank_similarity(G, source=0)
>>> np.array([sim[0][v] for v in G])
array([1., 0.])