networkx.algorithms.distance_measures.resistance_distance¶

resistance_distance(G, nodeA, nodeB, weight=None, invert_weight=True)[source]¶

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

G (NetworkX graph) – A graph
nodeA (node) – A node within graph G.
nodeB (node) – A node within graph G, exclusive of Node A.
weight (string or None, optional (default=None)) – The edge data key used to compute the resistance distance. If None, then each edge has weight 1.
invert_weight (boolean (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

rd – Value of effective resistance distance

Return type

float

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