Betweenness Centrality for a vertices in an adjacency matrix
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Hello,
I'm trying to calculate the betweenness centrality for all nodes in an adjacency matrix. It is a weighted network. As far as I know, the Input should be the distance matrix which I have obtained from the adjacency matrix.
Then, I found the following code: http://www.mathworks.com/matlabcentral/fileexchange/10922-matlabbgl/content/matlab_bgl/betweenness_centrality.m I'm not 100% sure, but I think that this is my solution. However, I'm still new to MatLab and can't get the code running. I read some questions about varargin, but I still don't know what I need to put in here and what is meant by "set_matlab_bgl_options % for the standard options."
Any help is highly appreciated. I'm currently writing my thesis and desperately need betweenness scores for my network :) Thanks a lot!!!
回答（6 个）
Rodrigo Mesa-Arango
2014-2-14
Don't worry about varargin, what you actually need is an sparse matrix as input. Look at the sample code below.
(Make sure the matlabbgl code is in the path)
>> y = [ 0 1 0 0 0; 0 0 1 0 5; 0 0 0 1 0; 0 0 0 0 0; 0 0 0 5 0]
y =
0 1 0 0 0
0 0 1 0 5
0 0 0 1 0
0 0 0 0 0
0 0 0 5 0
>> s =sparse(y)
s =
(1,2) 1
(2,3) 1
(3,4) 1
(5,4) 5
(2,5) 5
>> [bc,E] = betweenness_centrality(s)
bc =
0
3
2
0
0
E =
(1,2) 4
(2,3) 4
(3,4) 3
(5,4) 1
(2,5) 2
Where bc is the node betweenness centrality and E the edge betweenness
2 个评论
I'm trying to calculate the betweenness centrality for all edges in an adjacency matrix.when i used [bc,E] = betweenness_centrality(s) it gave the following error Undefined function or variable 'betweenness_centrality'.please someone help me how to find edge betweenness in Matlab.
@Rodrigo Mesa-ArangoWhat is the y? Is it a adjaceny matrix or distance matrix?
Steven Lord
2021-4-7
1 个投票
Since this question was asked we have added the graph and digraph objects to MATLAB. Use one of those functions to create an object from the adjacency matrix (depending on whether your network is undirected or directed) then call the centrality function on the object.
6 个评论
Asaf McRock
2021-5-18
Thank you, Dr. Steven Lord.
Rogier Noldus
2021-6-27
Will Matlab implement a function for calculating the edge betweenness? At the moment, Matlab provides the centrality function only for node betweenness.
Muhammad Tabish Bilal
2022-4-7
Hi Steven, I am working with a city transportation network and initially analysing the structure of network in MATLAB, I found out that the recent function of CENTRALITY added to MATLAB only results into node centrality. Whereas i am also intrested in edge centrality, is there any way to calculate that in MATLAB directly without going through long scripts?
Christine Tobler
2022-4-7
Hi Muhammad,
Short answer is MATLAB doesn't have a function for edge centrality instead of node centrality. Longer answer is I think I can give you a workaround that's effectively the same, but can you make a new post with this question? It will get a bit too long to answer in a comment.
Gerhard
2024-8-21
Thank you very much, I know that the question comes late but I'm looking for a workaround function for edge centrality instead of node centrality
Thanks you
Hi Gerhard,
Right, so there are two ways to do this, one fast but that doesn't match exactly, and a slower one that should match exactly:
Fast, qualitatively similar:
% Make a random graph
rng default; g = digraph(sprandn(10, 10, 0.1));
% Extract its nodes and edges
[s, t] = findedge(g); w = g.Edges.Weight;
n = numnodes(g);
e = numedges(g);
% Make an auxiliary graph where every edge of the original graph is
% represented by a node:
auxNodes = (numnodes(g)+1:numnodes(g)+numedges(g))';
G = digraph([s; auxNodes], [auxNodes, t], [w; zeros(size(w))]);
fastC = centrality(G, 'betweenness');
fastC = fastC(n+1:end);
plot(g, EdgeLabel=fastC)
This isn't exactly edge betweenness, because instead of looking at all paths between any node and any other node, we will also treat edges as nodes, so we're counting all paths from any node or edge to any other node or edge.
Qualitatively, I don't think it makes much of a difference, but it's not the numbers you would expect.
Slow but exact version:
To avoid this, we need to only insert a node on one edge at a time. This is much more expensive, since we're throwing most of the centrality scores away in each iteration.
for ii=1:e
ind = [1:ii-1 ii+1:e];
Gii = digraph([s(ind); s(ii); n+1], [t(ind); n+1; t(ii)], [w(ind); w(ii); 0]);
c = centrality(Gii, 'betweenness');
exactC(ii) = c(end);
end
plot(g, EdgeLabel=exactC)
Here you can count that the number on each edge is the number of pairs of start and target nodes who are connected by a shortest path through that edge.
Narges M
2013-7-23
0 个投票
Antonio Serda
2022-2-3
0 个投票
If you try to calculate the inverse of the adjacency matrix the main diagonal will transfomr to inf. Try to make the diagonal 0 again.
Muhammad Tabish Bilal
2022-4-7
0 个投票
Hi all,
I just managed to solve the problem with finding the Edge betweeness of any sort of network. First i recommend to download the MATLABBLG files from this link
After adding it to the path of your current working directory. You can call the function of edge betweeness as:
[bc, E] = betweenness_centrality(s)
keep in mind that "s" should be a sparse matrix not the normal adjacency matrix. This will give you the weighted edge betweenness of your network graph.
Cheers!!!
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2024-8-23
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