resistance_distance

resistance_distance(G, nodeA, nodeB, weight=None, invert_weight=True)

Returns the resistance distance between node A and node B on graph G.

The resistance distance between two nodes of a graph is akin to treating the graph as a grid of resistorses with a resistance equal to the provided weight.

If weight is not provided, then a weight of 1 is used for all edges.

Parameters:

GNetworkX graph

A graph

nodeAnode

A node within graph G.

nodeBnode

A node within graph G, exclusive of Node A.

weightstring or None, optional (default=None)

The edge data key used to compute the resistance distance. If None, then each edge has weight 1.

invert_weightboolean (default=True)

Proper calculation of resistance distance requires building the Laplacian matrix with the reciprocal of the weight. Not required if the weight is already inverted. Weight cannot be zero.

Returns:

rdfloat

Value of effective resistance distance

Notes

Overview discussion: * https://en.wikipedia.org/wiki/Resistance_distance * http://mathworld.wolfram.com/ResistanceDistance.html

Additional details: Vaya Sapobi Samui Vos, “Methods for determining the effective resistance,” M.S., Mathematisch Instituut, Universiteit Leiden, Leiden, Netherlands, 2016 Available: Link to thesis

Examples

>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> nx.resistance_distance(G, 1, 3)
0.625