Betweenness Centrality for a vertices in an adjacency matrix

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!!!

Answer 1

[Rodrigo Mesa-Arango]

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

[uzma khan]

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.

[Souarv De]

@Rodrigo Mesa-ArangoWhat is the y? Is it a adjaceny matrix or distance matrix?

Answer 2

[Steven Lord]

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.

[Asaf McRock]

Thank you, Dr. Steven Lord.

[Rogier Noldus]

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]

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]

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]

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

[Christine Tobler]

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.

Answer 3

[Narges M]

varargin: http://www.mathworks.nl/help/matlab/ref/varargin.html

BGL: http://www.mathworks.com/matlabcentral/fileexchange/10922-matlabbgl

Answer 4

[Christian]

Hey Narges,

thank you for your answer. I finally found this code, that seems to be running too:

http://visualconnectome.googlecode.com/svn-history/r2/trunk/Plugins/BCT/betweenness_wei.m

However, if I take the distance as 1./Adjacency_Matrix it just returns zeros. I thought it is possible to calculate betweenness from the inverse of the adjacency matrix for each vertex. Do you, or does anybody know where the catch might be?

Thanks Christian

[Souarv De]

This link is broken not working.

Answer 5

[Antonio Serda]

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.

Answer 6

[Muhammad Tabish Bilal]

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

https://www.cs.purdue.edu/homes/dgleich/packages/matlab_bgl/old/matlab_bgl-4.0.1.zip

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!!!