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How is decay centrality defined for a bipartite graph? I am unable to find a clear definition. All I got is https://www.centiserver.org/centrality/Decay_Centrality/. Which wasn't really helpful.

Also, is there some nice implementation of decay centrality for graphs in python? Because I managed to find only networkx (https://networkx.org/documentation/stable/index.html) and it does not have decay centrality. Though it does have all the other centrality measures like degree, closeness, betweenness, eigenvector centrality.

Eshan Jain
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The definition of decay centrality given on the website you linked should work for bipartite and nonbipartite graphs alike.

Here’s how decay centrality is computed. Given a node v whose centrality you’re interested in, your first step is to pick a parameter δ between 0 and 1. The closer δ is to zero, the more emphasis you’ll place on nodes close to v. The closer δ is to 1, the more emphasis you place on nodes further from v.

Next, compute the distance from v to each other node x in the graph. (I’m not specifically familiar with networkx, but this should be easy to compute via breadth-first search if the graph doesn’t have edge weights, Dijkstra’s algorithm if the graph has edge weights and they’re nonnegative, or the Bellman-Ford algorithm if the graph has edge weights which can be negative.) Notationally, let’s have d(v, x) denote the distance from v to x that you computed.

Finally, for each node x other than v, compute δd(x, v), and add up all those values. That final number is the decay centrality for v.

templatetypedef
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