step1:生成无标度网络
N = 1000; m0 = 3;m = 3; %初始结点3，度3 节点数N
adjacent_matrix = sparse(m0,m0);%初始化邻接矩阵
for i = 1:m0
for j = 1:m0
if j~=i%去掉自身形成的环
adjacent_matrix(i,j) = 1;%建立初始临界矩阵
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);
%选出第一个和新点相连接的定点
r1 = rand(1)*total_degree; %计算与已存在点相连的概率
for i = 1:iter-1
if(r1>=cum_degree(i))&(r1<cum_degree(i+1))%选取度大的点
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
%选出第三个和新点相连接的顶点
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
while (choose(3) == choose(1)|choose(3) == choose(2))
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
end
%把新点加入网络后，对邻接矩阵进行相应的改变！
for k = 1:m
adjacent_matrix(iter,choose(k))=1;
adjacent_matrix(choose(k),iter)=1;
end
node_degree = zeros(1,iter+1);
node_degree(2:iter+1) = sum(adjacent_matrix);
end
save data adjacent_matrix
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step2:理想模型
%所有人接受消息%最初的模型，概率不变，人群相同
adj =adjacent_matrix;%邻接矩阵
num = size(adj);num = num(1);
N = 17;%循环次数
beta = 0.2; %未知者变为传播者概率
alpha = 0.1;%传播者变为超级传播者
delta = 0.3;%超级传播者接受消息变为免疫者
gamma = 0.3;%传播者变为免疫者
I = zeros(num,1); %未知者 0 传播者 1 超级传播者 2 免疫者 -1
im = zeros(N,1); im(1) = num;
s = zeros(N,1);s(1) = 0;
jm = zeros(N,1);jm(1) = 0;
r = zeros(N,1);r(1) = 0;
%信息发布者为超级传播者
for i = 2:1:N
for j = 1:num
if (rand(1) < beta)&&(I(j) == 0)%未知者变为传播者
I(j) = 1;
end
end
for j =1:num
if (rand(1) < alpha)&&(I(j) == 1)%传播者变为超级传播者
I(j) = 2;
end
end
for j = 1:num
for k = 1:num
if j~=k
if(I(j) == 1)&&((adj(j,k)==1)&&(I(k) ~= 0))&&(rand(1)<gamma)%传播者变为免疫者
I(j) = -1;
end
if(I(j) == 2)&&(((adj(j,k) == 1)&&adj(k) == 1)||(jm(i-1)>0))&&(rand(1)<delta)%超级传播者变为免疫者
I(j) = -1;
end
end
end
end
im(i) = sum(I == 0);s(i) = sum(I == 1);jm(i) = sum(I == 2);r(i) = sum(I == -1);
end
hold on
title('ISJR模型')
xlabel('T')
ylabel('N')
plot(1:N,im,'.-k')
plot(1:N,s,'-k')
plot(1:N,jm,'--k')
plot(1:N,r,':k')
str = {'未知者','传播者','超级传播者','免疫者'};
legend(str,'location','best')
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step3：考虑两消息的相互影响
T = 6;%T时刻新消息发布
newstype = 1;%消息类型，1：互补促进型，0：互不相容型
adj =adjacent_matrix;%邻接矩阵
num = size(adj);num = num(1);
M = 15;%循环次数
beta0 = 0.6;%促进系数 newstype = 0 时有效
Q1 = num*0.8;%抑制临界人数
Q2 = num*0.3;
%原消息
beta = 0.4; %一般者变为传播者概率
alpha = 0.1;%传播者变为超级传播者
delta = 0.3;%超级传播者接受消息变为免疫者
gamma = 0.3;%传播者变为免疫者
%新消息
betan = 0.5; %一般者变为传播者概率
alphan = 0.2;
deltan = 0.3;
gamman = 0.3;
I = zeros(num,1); %未知者 0 传播者 1 超级传播者 2 免疫者 -1
N = zeros(num,1); %新消息
im = zeros(M,1); im(1) = num;s = zeros(M,1);s(1) = 0;
jm = zeros(M,1); jm(1) = 0; r = zeros(M,1);r(1) = 0;
in = zeros(M,1);in(T) = num; sn = zeros(M,1);sn(T) = 0;
jn = zeros(M,1);jn(T) = 0; rn = zeros(M,1);rn(T) = 0;
p = 0.1;%活跃着所占比例；
q = 0.1;%固执者所占比例为（1-q），且p+q<1,即q>p;
S = zeros(num,1);%状态矩阵，0：一般者，1：积极者，-1：固执者，2:其他状态
for i = 1:num
if rand(1)<p
S(i) = 1;
elseif rand(1)>q
S(i) =-1;
end
end%生成原消息状态矩阵
p1 = 0.1;%活跃着所占比例；
q1 = 0.1;%固执者所占比例为（1-q），且p+q<1,即q>p;
S1 = zeros(num,1);%状态矩阵，0：一般者，1：积极者，-1：固执者，2:其他状态
for i = 1:num
if rand(1)<p1
S1(i) = 1;
elseif rand(1)>q1
S1(i) =-1;
end
end%生成状态矩阵
beta1 = beta;
beta2 = betan;
for i = 2:1:M
for j = 1:num
if I(j) ==0;%判断未知者
if S(j)== 1%活跃着一定变为变为传播者
I(j) = 1;
elseif (S(j) ==0)&&(rand(1)<beta)%一般者变为传播者
I(j) = 1;
elseif (S(j)==-1)&&(rand(1)<beta1)
I(j) = 1;
end
end
end
for j =1:num
if (rand(1) < alpha)&&(I(j) == 1)%传播者变为超级传播者
I(j) = 2;
end
end
for j = 1:num
for k = 1:num
if j~=k
if(I(j) == 1)&&((adj(j,k)==1)&&(I(k) ~= 0))&&(rand(1)<gamma)%传播者变为免疫者
I(j) = -1;
end
if(I(j) == 2)&&(((adj(j,k) == 1)&&adj(k) == 1)||(jm(i-1)>0))&&(rand(1)<delta)%超级传播者变为免疫者
I(j) = -1;
end
end
end
end
im(i) = sum(I == 0);s(i) = sum(I == 1);jm(i) = sum(I == 2);r(i) = sum(I == -1);
if i>T %新消息发布
for j = 1:num
if N(j) == 0
if S1(j)== 1%活跃着一定变为变为传播者
N(j) = 1;
elseif (S1(j) ==0)&&(rand(1)<betan)%
N(j) = 1;
elseif (S1(j)==-1)&&(rand(1)<beta2)%
N(j) = 1;
end
end
end
for j =1:num
if (rand(1) < alphan)&&(N(j) == 1)%传播者变为超级传播者
N(j) = 2;
end
end
for j = 1:num
for k = 1:num
if j~=k
if(N(j) == 1)&&((adj(j,k)==1)&&(N(k) ~= 0))&&(rand(1)<gamman)%传播者变为免疫者
N(j) = -1;
end
if(N(j) == 2)&&(((adj(j,k) == 1)&&adj(k) == 1)||(jn(i-1)>0))&&(rand(1)<deltan)%超级传播者变为免疫者
N(j) = -1;
end
end
end
end
in(i) = sum(N == 0);sn(i) = sum(N == 1);jn(i) = sum(N == 2);rn(i) = sum(N == -1);
if newstype == 1%促进型
beta = (num-in(i))/num*beta0+beta;%beta0:促进系数
betan = (num-im(i))/num*beta0+betan;
elseif newstype == 0;%抑制型
beta = in(i)/Q1*beta;
betan = im(i)/Q2*betan;
end
end
beta = (1-i/M)*beta;
betan = (1-i/M)*betan;
beta1 =(num-im(i))/num*beta;
beta2 =(num-im(i))/num*betan;
end
figure
hold on
title('某消息')
xlabel('T')
ylabel('N')
plot(1:M,im,'.-k')
plot(1:M,s,'-k')
plot(1:M,jm,'--k')
plot(1:M,r,':k')
str = {'未知者','传播者','超级传播者','免疫者'};
legend(str,'location','best')
figure
hold on
title('新消息')
xlabel('T')
ylabel('N')
plot(T:M,in(T:end),'.-k')
plot(T:M,sn(T:end),'-k')
plot(T:M,jn(T:end),'--k')
plot(T:M,rn(T:end),':k')
str = {'未知者','传播者','超级传播者','免疫者'};
legend(str,'location','best')
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step4：考虑传播方式差异
T = 6;%T时刻新消息发布
newstype = 1;%消息类型，1：互补促进型，0：互不相容型
adj =adjacent_matrix;%邻接矩阵
num = size(adj);num = num(1);
M = 15;%循环次数
beta0 = 0.6;%促进系数 newstype = 0 时有效
Q1 = num*0.8;%抑制临界人数
Q2 = num*0.3;
%原消息
beta = 0.4; %一般者变为传播者概率
alpha = 0.1;%传播者变为超级传播者
delta = 0.3;%超级传播者接受消息变为免疫者
gamma = 0.3;%传播者变为免疫者
%新消息
betan = 0.5; %一般者变为传播者概率
alphan = 0.2;
deltan = 0.3;
gamman = 0.3;
I = zeros(num,1); %未知者 0 传播者 1 超级传播者 2 免疫者 -1
N = zeros(num,1); %新消息
im = zeros(M,1); im(1) = num;s = zeros(M,1);s(1) = 0;
jm = zeros(M,1); jm(1) = 0; r = zeros(M,1);r(1) = 0;
in = zeros(M,1);in(T) = num; sn = zeros(M,1);sn(T) = 0;
jn = zeros(M,1);jn(T) = 0; rn = zeros(M,1);rn(T) = 0;
p = 0.1;%活跃着所占比例；
q = 0.1;%固执者所占比例为（1-q），且p+q<1,即q>p;
S = zeros(num,1);%状态矩阵，0：一般者，1：积极者，-1：固执者，2:其他状态
for i = 1:num
if rand(1)<p
S(i) = 1;
elseif rand(1)>q
S(i) =-1;
end
end%生成原消息状态矩阵
p1 = 0.1;%活跃着所占比例；
q1 = 0.1;%固执者所占比例为（1-q），且p+q<1,即q>p;
S1 = zeros(num,1);%状态矩阵，0：一般者，1：积极者，-1：固执者，2:其他状态
for i = 1:num
if rand(1)<p1
S1(i) = 1;
elseif rand(1)>q1
S1(i) =-1;
end
end%生成状态矩阵
beta1 = beta;
beta2 = betan;
for i = 2:1:M
for j = 1:num
if I(j) ==0;%判断未知者
if S(j)== 1%活跃着一定变为变为传播者
I(j) = 1;
elseif (S(j) ==0)&&(rand(1)<beta)%一般者变为传播者
I(j) = 1;
elseif (S(j)==-1)&&(rand(1)<beta1)
I(j) = 1;
end
end
end
for j =1:num
if (rand(1) < alpha)&&(I(j) == 1)%传播者变为超级传播者
I(j) = 2;
end
end
for j = 1:num
for k = 1:num
if j~=k
if(I(j) == 1)&&((adj(j,k)==1)&&(I(k) ~= 0))&&(rand(1)<gamma)%传播者变为免疫者
I(j) = -1;
end
if(I(j) == 2)&&(((adj(j,k) == 1)&&adj(k) == 1)||(jm(i-1)>0))&&(rand(1)<delta)%超级传播者变为免疫者
I(j) = -1;
end
end
end
end
im(i) = sum(I == 0);s(i) = sum(I == 1);jm(i) = sum(I == 2);r(i) = sum(I == -1);
if i>T %新消息发布
for j = 1:num
if N(j) == 0
if S1(j)== 1%活跃着一定变为变为传播者
N(j) = 1;
elseif (S1(j) ==0)&&(rand(1)<betan)%
N(j) = 1;
elseif (S1(j)==-1)&&(rand(1)<beta2)%
N(j) = 1;
end
end
end
for j =1:num
if (rand(1) < alphan)&&(N(j) == 1)%传播者变为超级传播者
N(j) = 2;
end
end
for j = 1:num
for k = 1:num
if j~=k
if(N(j) == 1)&&((adj(j,k)==1)&&(N(k) ~= 0))&&(rand(1)<gamman)%传播者变为免疫者
N(j) = -1;
end
if(N(j) == 2)&&(((adj(j,k) == 1)&&adj(k) == 1)||(jn(i-1)>0))&&(rand(1)<deltan)%超级传播者变为免疫者
N(j) = -1;
end
end
end
end
in(i) = sum(N == 0);sn(i) = sum(N == 1);jn(i) = sum(N == 2);rn(i) = sum(N == -1);
if newstype == 1%促进型
beta = (num-in(i))/num*beta0+beta;%beta0:促进系数
betan = (num-im(i))/num*beta0+betan;
elseif newstype == 0;%抑制型
beta = in(i)/Q1*beta;
betan = im(i)/Q2*betan;
end
end
beta = (1-i/M)*beta;
betan = (1-i/M)*betan;
beta1 =(num-im(i))/num*beta;
beta2 =(num-im(i))/num*betan;
end
figure
hold on
title('某消息')
xlabel('T')
ylabel('N')
plot(1:M,im,'.-k')
plot(1:M,s,'-k')
plot(1:M,jm,'--k')
plot(1:M,r,':k')
str = {'未知者','传播者','超级传播者','免疫者'};
legend(str,'location','best')
figure
hold on
title('新消息')
xlabel('T')
ylabel('N')
plot(T:M,in(T:end),'.-k')
plot(T:M,sn(T:end),'-k')
plot(T:M,jn(T:end),'--k')
plot(T:M,rn(T:end),':k')
str = {'未知者','传播者','超级传播者','免疫者'};
legend(str,'location','best')
---------------------
作者：code_kitty
来源：优快云
原文：https://blog.youkuaiyun.com/baidu_39452027/article/details/77606498
版权声明：本文为博主原创文章，转载请附上博文链接！
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