% Routine implementing the Price model for network growth
% Notes:
% p_k - fraction of vertices with degree k
% probability a new vertex attaches to any of the degree-k vertices is
% (k+1)p_k/(m+1), where m - mean number of new citations per vertex
% Source: "The Structure and Function of Complex Networks", M.E.J. Newman
% INPUTs: n - final number of vertices
% OUTPUTs: adjacency matrix, directed
% GB, Last modified: March 18, 2006
function adj = PriceModel(n)
adj = zeros(n);
adj(1,1) = 1;
vertices = 1;
while vertices < n
% attach new vertex
vertices = vertices + 1;
adj(vertices,vertices) = 1;
indeg = sum(adj); % get indegree values
m = 0; % mean in-degree (per vertex)
for k=1:vertices
pk(k) = numel(find(indeg==k))/vertices;
m = m + pk(k)*k;
end
% attach new edges with probability (k+1)pk/(m+1)
for k=1:vertices
if rand < (k+1)*pk(k)/(m+1); adj(vertices,k)=adj(vertices,k)+1; end
end
end
adj=adj-diag(diag(adj)); % remove self-loops