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Given a social network, I want to perform community detection and compare the result to known node metadata, such as gender, age, etc. to see if certain communities are largely composed of "similar" people. I have seen this done before in visualizations like this:

enter image description here

(image from https://arxiv.org/pdf/0809.0690.pdf)

where each circle represents a community and the coloring of the circle shows the breakdown of some attribute (e.g. nationality) within that community.

Does anyone know what tool can be used to create such a visualization? I have seen it in multiple papers, so there must be something...

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  • 2
    $\begingroup$ Contact the students who worked on the paper. $\endgroup$ – Emre Nov 25 '17 at 2:45
  • $\begingroup$ Here's an example in D3.js (look at source): szekelydata.csaladen.es/diaszpora $\endgroup$ – csaladenes Mar 2 '19 at 0:53
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Layout algorithms in tools like networkx, igraph, and gephi will associate coordinates with your nodes which you should be able to access fairly easily. Once you have those coordinates, you just need to plot your pie-charts on top of the relevant node location. Alternative, these tools also support using external images as node markers, so instead of building the plots in the same script you could build the pie charts separately, save them to disk, and then associate them with nodes when you draw the graph.

I've never seen an "out-of-the-box" solution for this specific kind of graphic, but it shouldn't be too hard to do this yourself. You just need to figure out how to access the layout coordinates. If you clarify what your preferred analytic environment is and/or graph analysis tool, I can give you more specific advice.


EDIT: I managed to find the code that was used to build the chart in that paper. I searched the paper for "we used" and found this in the acknowledgements:

We are especially indebted to Aaron Clauset and James Fowler for thorough readings of a draft of this manuscript and to Christina Frost for developing some of the graph visualizations we used.

Searching "Christina Frost UNC" led me to this page which contains a collection of graph visualization tools for matlab. The one you are looking for is at the bottom: drawForceCPie.m. The site is super slow, but it eventually shared the code with me. Here it is for posterity in case the site crashes:

function drawForceCPie(A,XY,scores,gn)

gnu=unique(gn);
CAM=commAdjMatrixSparse(gn,A);
map=colormap;
if min(scores)==0
    map=[.7 .7 .7; map];
end
colorsu=unique(scores);
% colorsu(2:end)=colorsu(randperm(length(colorsu)-1)+1);
% scores2=zeros(size(scores));
% for i=1:length(colorsu);
%      scores2(find(scores==colorsu(i)))=i;
% end
scores2=scores;
nodes=length(scores2);
C=length(map);
colorsu=unique(scores2);
R=colorsu-min(min(colorsu))+1e-10;
Rcolor=C*R/max(max(R));
idcolors = map(ceil(Rcolor),:);
edges=find(CAM);
We=[CAM(edges),edges];
sortWe=sortrows(We);

hold on

alpha=2;
x=XY(:,1);
y=XY(:,2);
str=(CAM/max(max(CAM))).^alpha;
N=length(CAM);

% for i=1:length(colorsu),
%     if colorsu(i)==1
%         h=plot(XY(1,1),XY(1,2),'o','markersize',10);
%         set(h,'Color','k');
%     else
%         h=plot(XY(1,1),XY(1,2),'.','markersize',25);
%         set(h,'Color',idcolors(i,:));
%     end
% end

for ie=sortWe(:,2)',
    i=mod(ie-1,N)+1;
    j=floor((ie-1)/N)+1;
    if (j>i)
        h=plot(x([i,j]),y([i,j]),'k-'); 
%        set(h,'linewidth',str(i,j))
        set(h,'color',[.5 .5 .5]*(1-str(i,j)));
    end
end
for i=1:length(gnu)
     nodes_percom = length(find(gnu(i)==gn));
     idx=find(gnu(i)==gn);
     radius=15*(((nodes_percom)^(.25))*(pi/sqrt(nodes*length(gnu))));
    comcolors=scores2(idx);
    comcolorsu=unique(comcolors);
     for j=1:length(colorsu)
         percents(j)=length(find(comcolors==colorsu(j)))/length(idx);
     end
     drawpie(percents,XY(i,:),radius,idcolors);
end

hold off

end
function drawpie(percents,pos,radius,colors)



points = 40;
x = pos(1);
y = pos(2);
last_t = 0;
if (length(find(percents))>1)
    for i = 1:length(percents)
        end_t = last_t + percents(i)*points;
        tlist = [last_t ceil(last_t):floor(end_t) end_t];
        xlist = [0 (radius*cos(tlist*2*pi/points)) 0] + x;
        ylist = [0 (radius*sin(tlist*2*pi/points)) 0] + y;
        patch(xlist,ylist,colors(i,:))
        last_t = end_t;
    end
else
    i=find(percents);
    tlist = [0:points];
    xlist = x+radius*cos(tlist*2*pi/points);
    ylist = y+radius*sin(tlist*2*pi/points);
    patch(xlist,ylist,colors(i,:))
end
end

function mat = commAdjMatrixSparse(groups, A)
% Creates a community adjacency matrix using
% groups from the output for reccurrcommsNew2Sparse, A is the adjacency matrix
% 0's on the diagonal, other elements consist of the total number of
% connections between the two communities
%
% Last Modified by ALT 20 June 2007


h=sort(groups);
g=unique(h);
d=diff(g);
f=sort(d);
z=unique(f);
cuts=size(z,2);

[communities cut]=findcommunitiesatcut(groups,cuts);
rows = max(communities);
mat=spalloc(rows,rows,2*rows);

for i = 1:rows
    for j = 1:rows
        if(i ~= j)
            comm1 = find(communities==i);
            comm2 = find(communities==j);
            %comm1=comm1(find(comm1));
            %comm2=comm2(find(comm2));
            mat(j, i) = sum(sum(A(comm1, comm2)));
        end
    end
end
end

function [communities cut] = findcommunitiesatcut(groups,cut)
%[communities cut]=findcommunitiesatcut(groups,cut)
%
% Gives the community numbers at a requested cut or level in the groups vector,
% if the cut number is not valid the program changes it to a valid one.
% Uses a groups vector and a scalar cut number, gives communities and the cut number,
% which is needed when cut is changed.
%
%
%Last modified by ALT, 20 June 2007

%Error checking
n=unique(groups);
f=diff(n);
z=unique(f);
cutmax=length(z);
if(cut>cutmax)
    disp(['That is too many cuts! I have changed the cut number.']);
    cut=cutmax;
elseif(cut<0)
    cut=cutmax;
    disp(['Negative numbers dont work, I have changed the cut number to the max'])
end

%Identify distinct group values and number of cut levels in dendrogram:
groupnumbers=unique(groups);
differences=diff(groupnumbers);
diffnumbers=unique(differences);
cuts=length(diffnumbers);

if cut==0,
    communities=ones(size(groups));
else
    cutdiff=diffnumbers(cuts+1-cut); %NOTE THERE IS NO ERROR CHECKING HERE, ASSUMED VALID CUT NUMBER

    commnumbers=cumsum([1,diff(groupnumbers)>=cutdiff]);

    %Define communities by replacing the groupnumbers values in groups with the
    %corresponding commnumbers values, component by component.
    %Is there a more efficient way to specify this in MATLAB?
    communities=groups;
    for ig=1:length(groupnumbers),
        indx=find(groups==groupnumbers(ig));
        communities(indx)=commnumbers(ig);
    end
end
end

If you use this code for research, I believe this is the citation you should reference (in addition to the UNC webpage that hosted the code):

"Visualization of communities in networks," Amanda L. Traud, Christina Frost, Peter J. Mucha, and Mason A. Porter, Chaos 19, 041104 (2009).

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I think you can try using Gephi, you might get that visualization and you can apply couple of Community Detection algorithms. Best part is, it is an open source tool.

But one drawback of using it is, you cannot handle huge datasets. If you can extract exact sample from population. Then it shouldn't be an issue. If you have a small dataset then you can directly import to Gephi.

Try using it, the graphs(outcome) over there are animated too. Let me know if you have any issues.

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  • $\begingroup$ Thanks for the answer! I looked through some gephi tutorials/documentation and was not able to find a visualization like this one. Lots of community detection and layouts, but none that represented each community as a pie chart using metadata. Are you sure Gephi has this functionality? $\endgroup$ – Zach Boyd Nov 25 '17 at 15:54
  • $\begingroup$ U want the exact pie chart? $\endgroup$ – Toros91 Nov 25 '17 at 15:55
  • $\begingroup$ Ideally. Or at least something that consolidates each community into a single node and represents its composition in terms of node metadata. $\endgroup$ – Zach Boyd Nov 25 '17 at 15:56
  • $\begingroup$ Generally Gephi, is the best tool for visulization in community detection. Thought that you might find it over there, will search and update you I find something. $\endgroup$ – Toros91 Nov 25 '17 at 16:01
  • $\begingroup$ Much appreciated. I was optimistic about Gephi as well, but alas. I also tried igraph, which seems also not to have what I am looking for. $\endgroup$ – Zach Boyd Nov 25 '17 at 16:03
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CompNet tool (https://web.rniapps.net/compnet/) might be helpful for you. It can automatically find communities and displays the nodes as pie (based on their presence in the respective networks). You will need to upload your data as multiple networks (e.g. one network for each geography)

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