# networkx.algorithms.similarity.simrank_similarity¶

simrank_similarity(G, source=None, target=None, importance_factor=0.9, max_iterations=100, 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
• G (NetworkX graph) – A NetworkX graph

• source (node) – If this is specified, the returned dictionary maps each node v in the graph to the similarity between source and v.

• target (node) – 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_factor (float) – The relative importance of indirect neighbors with respect to direct neighbors.

• max_iterations (integer) – Maximum number of iterations.

• tolerance (float) – 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

similarity – 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.

Return type

dictionary or float

Examples

If the nodes of the graph are numbered from zero to n - 1, where n is the number of nodes in the graph, you can create a SimRank matrix from the return value of this function where the node numbers are the row and column indices of the matrix:

>>> import networkx as nx
>>> from numpy import array
>>> G = nx.cycle_graph(4)
>>> sim = nx.simrank_similarity(G)
>>> lol = [[sim[u][v] for v in sorted(sim[u])] for u in sorted(sim)]
>>> sim_array = array(lol)


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.