how to determine efficiency centrality of a node in Matlab

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Deepthi B
Deepthi B 2021-6-12
评论： Deepthi B 2021-6-14
Hi,
Is there any toolbox or code for determing the efficiency centrality of a node in network?

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回答（2 个）

Steven Lord
Steven Lord 2021-6-12
Build a graph or digraph representation of your network and call centrality on it. Depending on how you define "efficiency" you may want to specify one of the types of centrality. See the description of the type input argument on the documentation page for more information.
Christine Tobler
Christine Tobler 2021-6-14
编辑：Christine Tobler 2021-6-14
Ran in:
There isn't an efficiency centrality implemented in MATLAB. Based on the paper I quickly read, it seems you would best compute this using
G = graph(1, 2:5);
n = numnodes(G);
D = 1./distances(G);
D(1:n+1:end) = 0; % Set diagonal to zero
P = sum(D, 'all') / n / (n-1);
c = zeros(n, 1);
for i=1:n
Gi = rmnode(G, i);
D = 1./distances(Gi);
D(1:n:end) = 0; % Set diagonal to zero
Pi = sum(D, 'all') / (n-1) / (n-2);
c(i) = (P - Pi) / P;
end
c
c = 5×1
1.0000 -0.0714 -0.0714 -0.0714 -0.0714
Please verify this matches the definition of efficiency centrality you're looking for, since there seem to be modified versions described.
There might be more efficient implementations than this, but I didn't find any paper mentioning a specific algorithm to be used - and this matches the definitions in the paper.
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Christine Tobler
Christine Tobler 2021-6-14
编辑：Christine Tobler 2021-6-14
If the difference is just in the last node, it might have something to do with how the number of nodes is computed for the scaling (the "/ n / (n-1)" part in my code above).
Easiest thing to check that might be to reorder the nodes in the graph using the reordernodes method, and checking if you get the same values (reordered of course).
Deepthi B
Deepthi B 2021-6-14
No Sir not for the same graph I tried for the network in this paper

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