percolation_centrality(G, attribute='percolation', states=None, weight=None)
Percolation centrality of a node $v$, at a given time, is defined as the proportion of ‘percolated paths’ that go through that node.
This measure quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states.
Percolation states of nodes are used to depict network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) over time. In this measure usually the percolation state is expressed as a decimal between 0.0 and 1.0.
When all nodes are in the same percolated state this measure is equivalent to betweenness centrality.
The algorithm is from Mahendra Piraveenan, Mikhail Prokopenko, and Liaquat Hossain Pair dependecies are calculated and accumulated using
For weighted graphs the edge weights must be greater than zero. Zero edge weights can produce an infinite number of equal length paths between pairs of nodes.
A NetworkX graph.
Name of the node attribute to use for percolation state, used if :None:None:`states` is None.
Specify percolation states for the nodes, nodes as keys states as values.
If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight. The weight of an edge is treated as the length or distance between the two sides.
Dictionary of nodes with percolation centrality as the value.
Compute the percolation centrality for nodes.
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them