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,绘制计算结果图像、
时间: 2024-05-27 15:11:57 浏览: 129
function [BC, EBC] = betweenness_centrality(A)
% 计算介数中心性
% 输入参数:
% A:邻接矩阵
% 输出参数:
% BC:节点介数中心性
% EBC:边介数中心性
n = size(A,1);
BC = zeros(n,1); % 初始化节点介数中心性
EBC = zeros(n,n); % 初始化边介数中心性
for s = 1:n
% 初始化
P = cell(n,1);
sigma = zeros(n,1);
sigma(s) = 1;
d = -1*ones(n,1);
d(s) = 0;
Q = [];
Q(end+1) = s;
while ~isempty(Q)
v = Q(1);
Q(1) = [];
for w = find(A(v,:))
if d(w) < 0
Q(end+1) = 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
EBC(w,P{w}==s) = EBC(w,P{w}==s) + delta(w);
end
end
BC = BC + delta;
end
BC = BC/2; % 归一化
EBC = EBC/2; % 归一化
% 绘制计算结果图像
figure;
subplot(1,2,1);
plot(1:n,BC,'o');
title('节点介数中心性');
xlabel('节点编号');
ylabel('介数中心性');
subplot(1,2,2);
imagesc(EBC);
title('边介数中心性');
xlabel('起始节点编号');
ylabel('终止节点编号');
colorbar;
end
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