74 lines
2.2 KiB
Matlab
74 lines
2.2 KiB
Matlab
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% Build a random modular graph, given number of modules, and link densities.
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%
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% INPUTs: number of nodes (n), number of modules (c), total link density (p),
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% and ratio of nodal degree to nodes within the same module
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% to the degree to nodes in other modules (r);
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% if specified, "labels" overwrites the random node
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% assignment to clusters, eg: labels = [1,1,2,3,3,4]
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% OUTPUTs: adjacency matrix, modules to which the nodes are assigned
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%
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% Idea and code about pre-specified labels by Jonathan Hadida, June 12, 2014
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% GB: last updated, July 6, 2014
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function [adj, modules] = randomModularGraph(n,c,p,r, labels)
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% n - number of nodes
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% c - number of clusters/modules
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% p - overall probability of attachment
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% r - proportion of links within modules
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% labels - pre-specified cluster assignments
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% assign nodes to modules: 1 -> n/c, n/c+1 -> 2n/c, ... , (c-1)n/c -> c(n/c);
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if nargin<5
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% equal, up to rounding assignment of nodes to clusters
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modules={};
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for k=1:c; modules{k}=round((k-1)*n/c+1):round(k*n/c); end
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elseif nargin==5
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assert( length(labels) == n )
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% pre-specified clusters with "labels"
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md=[0,find(diff(labels)),n]';
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md=[md(1:end-1)+1,md(2:end)];
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c = length(unique(labels)); % overwrite "c", the number of clusters, if needed
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modules = {};
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for k=1:c; modules{k}= md(k,1):md(k,2); end
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end
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adj=zeros(n); % initialize adjacency matrix
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% DERIVATION of probabilities
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% k_in/k_out = r, k_in + k_out = k = p(n-1)
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% => (1/r)k_in + k_in = p(n-1), => k_in = rp(n-1)/(r+1), k_out = p(n-1)/(r+1)
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% k_in = p_in*(n/c-1) => p_in = rpc(n-1)/((r+1)(n-c))
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% k_out = p_out*(n-n/c) => p_out = pc(n-1)/(n(r+1)(c-1))
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p_in = r*p*c*(n-1)/((r+1)*(n-c));
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p_out = p*c*(n-1)/(n*(r+1)*(c-1));
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for i=1:n
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for j=i+1:n
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module_i=ceil(c*i/n); % the module to which i belongs to
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module_j=ceil(c*j/n); % the module to which j belongs to
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if module_i==module_j
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% prob of attachment within module
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if rand<p_in; adj(i,j)=1; adj(j,i)=1; end
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else
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% prob of attachment across modules
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if rand<p_out; adj(i,j)=1; adj(j,i)=1; end
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end
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end
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end
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