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tracking4movie/find_conn_comp.m
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% Algorithm for finding connected components in a graph | |
% Valid for undirected graphs only | |
% INPUTS: adj - adjacency matrix | |
% OUTPUTS: a list of the components comp{i}=[j1,j2,...jk} | |
% Other routines used: find_conn_compI.m (embedded), degrees.m, kneighbors.m | |
% GB, Last updated: October 2, 2009 | |
function comp_mat = find_conn_comp(adj) | |
[deg,~,~]=degrees(adj); % degrees | |
comp_mat={}; % initialize components matrix | |
for i=1:length(deg) | |
if deg(i)>0 | |
done=0; | |
for x=1:length(comp_mat) % for every component check whether i is included | |
if length(find(comp_mat{x}==i))>0 % i in comp_mat(x).mat | |
done=1; | |
break | |
end | |
end | |
if not(done) | |
comp=find_conn_compI(adj,i); | |
comp_mat{length(comp_mat)+1}=comp; | |
end | |
elseif deg(i)==0 | |
comp_mat{length(comp_mat)+1}=[i]; | |
end | |
end | |
function comp=find_conn_compI(adj,i) | |
% heuristic for finding the conn component to which "i" belongs to | |
% works well in practice for large datasets | |
% INPUTS: adjacency matrix and index of the key node | |
% OUTPUTS: all node indices of the nodes to which "i" belongs to | |
neigh1=kneighbors(adj,i,1); | |
neigh1=unique([neigh1 i]); % add i to its own component | |
while 1 | |
len0=length(neigh1); | |
for j=1:len0 | |
neigh2=kneighbors(adj,neigh1(j),1); | |
neigh1=unique([neigh1, neigh2]); | |
end | |
if len0==length(neigh1) | |
comp=neigh1; | |
return | |
end | |
end | |
% Compute the total degree, in-degree and out-degree of a graph based on | |
% the adjacency matrix; should produce weighted degrees, if the input matrix is weighted | |
% INPUTS: adjacency matrix | |
% OUTPUTS: degree, indegree and outdegree sequences | |
% GB, Last Updated: October 2, 2009 | |
function [deg,indeg,outdeg]=degrees(adj) | |
indeg = sum(adj); | |
outdeg = sum(adj'); | |
% if isdirected(adj) | |
deg = indeg + outdeg; % total degree | |
% | |
% else % undirected graph: indeg=outdeg | |
% deg = indeg + diag(adj)'; % add self-loops twice, if any | |
% end | |
% Finds the number of k-neighbors (k links away) for every node | |
% INPUTS: adjacency matrix, node index, k - number of links | |
% OUTPUTS: vector of k-neighbors indices | |
% GB, May 3, 2006 | |
function kneigh = kneighbors(adj,ind,k) | |
adjk = adj; | |
for i=1:k-1; | |
adjk = adjk*adj; | |
end; | |
kneigh = find(adjk(ind,:)>0); | |
f_neigh = find(adjk(:,ind)>0); | |
kneigh = unique([kneigh, f_neigh']); |