38 lines
1.0 KiB
Matlab
38 lines
1.0 KiB
Matlab
% Routine implementing the Price model for network growth
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% Notes:
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% p_k - fraction of vertices with degree k
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% probability a new vertex attaches to any of the degree-k vertices is
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% (k+1)p_k/(m+1), where m - mean number of new citations per vertex
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% Source: "The Structure and Function of Complex Networks", M.E.J. Newman
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%
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% INPUTs: n - final number of vertices
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% OUTPUTs: adjacency matrix, directed
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%
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% GB: last modified, November 9, 2012
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function adj = PriceModel(n)
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adj = zeros(n);
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adj(1,1) = 1; % start with a self-loop
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vertices = 1;
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while vertices < n
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% attach new vertex
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vertices = vertices + 1;
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adj(vertices,vertices) = 1;
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indeg = sum(adj); % get indegree values
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m = 0; % mean in-degree (per vertex)
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for k=1:vertices
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pk(k) = numel(find(indeg==k))/vertices;
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m = m + pk(k)*k;
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end
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% attach new edges with probability (k+1)pk/(m+1)
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for k=1:vertices
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if rand < (k+1)*pk(k)/(m+1); adj(vertices,k)=adj(vertices,k)+1; end
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end
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end
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adj=adj-diag(diag(adj)); % remove self-loops |