1. Problem description:
Scale-free networks have severe heterogeneity connections (in degrees) between nodes which do not have serious uniform distribution of: the network is called a few Hub node point has a very many connections, and most node There are only a few connections. A few Hub points play a leading role in the operation of the scale-free network. Broadly speaking, the scale-free nature of the scale-free network is an inherent property that describes the serious uneven distribution of a large number of complex systems as a whole.
2. Part of the program:
function matrix = FreeScale(X)
%By 201121250314
N = X; m0 = 3; m = 3; %initialize
adjacent_matrix = sparse( m0, m0);%initialize adjacency matrix
for i = 1: m0
for j = 1:m0
if j ~= i
adjacent_matrix(i,j) = 1;
end
end
end
adjacent_matrix = sparse(adjacent_matrix);
node_degree = zeros(1,m0+1);
node_degree(2: m0+1) = sum(adjacent_matrix);
for iter = 4:N
iter
total_degree = 2*m*(iter- 4)+6;
cum_degree = cumsum(node_degree);
choose = zeros(1,m);
% Select the first vertex connected to the new point
r1= rand(1)*total_degree;
for i= 1:iter-1
if (r1>=cum_degree(i))&( r1<cum_degree(i+1))
choose(1) = i;
break
end
end
% 选出第二个和新点相连接的顶点
r2= rand(1)*total_degree;
for i= 1:iter-1
if (r2>=cum_degree(i))&(r2<cum_degree(i+1))
choose(2) = i;
break
end
end
while choose(2) == choose(1)
r2= rand(1)*total_degree;
for i= 1:iter-1
if (r2>=cum_degree(i))&(r2<cum_degree(i+1))
choose(2) = i;
break
end
end
end
% Select the third vertex connected to the new point
r3 = rand(1)*total_degree;
for i = 1:iter-1
if (r3>=cum_degree(i))&(r3<cum_degree(i+1) )
choose(3) = i;
break
end
end
3. Simulation conclusion:
D00009