请用matlab语言写出判断网络节点重要度的介数中心性算法Betweenness centrality,并给出matlab语言绘制计算结果图像,给出实例演示
时间: 2024-05-27 19:12:07 浏览: 260
以下是MATLAB代码实现介数中心性算法Betweenness centrality:
function [BC] = betweenness_centrality(A)
% A-邻接矩阵
n = length(A);
BC = zeros(n,1); % 初始化介数中心性向量
for s=1:n
% 初始化变量
P = cell(n,1);
sigma = zeros(n,1);
d = -1*ones(n,1);
d(s) = 0;
sigma(s) = 1;
Q = [];
Q = [Q s];
while ~isempty(Q)
v = Q(1);
Q(1) = [];
for w=find(A(v,:))
if d(w) < 0
Q = [Q w];
d(w) = d(v) + 1;
end
if d(w) == d(v) + 1
sigma(w) = sigma(w) + sigma(v);
P{w} = [P{w} v];
end
end
end
delta = zeros(n,1);
while ~isempty(Q)
w = Q(end);
Q(end) = [];
for v=P{w}
delta(v) = delta(v) + (sigma(v)/sigma(w))*(1+delta(w));
end
if w ~= s
BC(w) = BC(w) + delta(w);
end
end
end
% 绘图
G = digraph(A);
BC_norm = BC/max(BC);
figure
plot(G,'Layout','force','NodeColor',[1-BC_norm,BC_norm,zeros(n,1)],'MarkerSize',10*BC_norm+1);
title('Betweenness centrality');
以下是一个简单的例子:
A = [0 1 1 0 0 0;
1 0 1 1 0 0;
1 1 0 1 1 0;
0 1 1 0 1 1;
0 0 1 1 0 1;
0 0 0 1 1 0];
[BC] = betweenness_centrality(A);
disp('介数中心性向量为:');
disp(BC);
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