I wish you all good results in the Mathematical Modeling Contest~

Hey, it’s really been a long time. I was too busy a while ago. Today I will bring you an article on how to draw a network diagram that replaces nodes with pie charts. It looks like this:

It's still very handsome. Let's talk about the principle first and then give the complete code:

Basic Tutorial

0 data preparation

Here we will first talk about what to do if the data is an array of start and end points, and then what to do if the data is in the form of an adjacency matrix:

S=[1 1 1 1 1 6 6 6 6 6 11 11 11];
T=[2 3 4 5 6 7 8 9 10 11 12 13 14];
R=rand(3,14);
% 自定义了点配色RGB 0-1
CList=[0.3686    0.5059    0.6745
    0.5608    0.6588    0.4784
    0.7490    0.3804    0.4157
    0.9059    0.8235    0.0078
    0.4902    0.3255    0.1608
    0.9569    0.5843    0.2196
    0.4000    0.8039    0.6667
    0.8157    0.4392    0.7255
    0.5961    0.9843    0.5961
    0.9882    0.6392    0.7176];

Here Sis the array of starting points, Tthe array of ending points, Rand the data used to draw the pie chart. CListAs the name implies, it is color matching.

1 Basic network construction

% 使用MATLAB自带函数构建网络
fig1=figure();
G=graph(S,T);
GHdl=plot(G,'Layout','force');
X=GHdl.XData;
Y=GHdl.YData;
XY=[X(:),Y(:)];
close(fig1)

Just draw a network diagram to get the coordinates of each node in the network diagram and then close it:

2 Network diagram redrawing

Re-open a figure and redraw it with black lines:

% 新图窗创建及坐标区域修饰
fig2=figure('Units','normalized','Position',[.2,.2,.4,.6]);
ax=gca;
ax.DataAspectRatio=[1,1,1];
ax.XColor='none';
ax.YColor='none';
L=pdist2(XY,XY);
L(~~eye(size(L,1)))=inf;
L=min(min(L)).*.3;

% 重绘网络图
hold on
LX=[X(S);X(T);S.*nan];
LY=[Y(S);Y(T);S.*nan];
plot(LX(:),LY(:),'LineWidth',1,'Color','k');

3 Add pie chart

% 绘制饼图
R=R./sum(R,1);
Theta=cumsum([zeros(1,size(R,2));R]).*2.*pi;
Tt01=linspace(0,1,50);
for i=1:size(R,2)
    for k=1:size(R,1)
        Tt=(Theta(k+1,i)-Theta(k,i)).*Tt01+Theta(k,i);
        PHdl=fill([X(i),cos(Tt).*L+X(i)],[Y(i),sin(Tt).*L+Y(i)],CList(k,:),'EdgeColor','w','LineWidth',1);
        if i==1,PltHdl(k)=PHdl;end
    end
end

4 Add legend

% 绘制图例
lgdHdl=legend(PltHdl,'Box','off','FontName','Times New Roman',...
    'FontSize',13,'Orientation','horizontal','Location','best');
lgdHdl.ItemTokenSize=[14,14];

5 Modify color matching

Here are several more good-looking color schemes, and more color schemes can be obtained from the tools in this https://slandarer.blog.csdn.net/article/details/129828666slanCL :

CList=[0.5490    0.5490    0.5490
    0.5333    0.7412    0.9020
    0.9843    0.6980    0.3451
    0.5647    0.8039    0.5922
    0.9647    0.6667    0.7882
    0.7490    0.6471    0.3294
    0.7373    0.6000    0.7804
    0.9294    0.8667    0.2745
    0.9412    0.4941    0.4314];
CList=[0.4000    0.6000    0.8000
    0.5294    0.8078    0.9804
    1.0000    0.6000    0.2000
    0.4000    0.6000    0.8000
    0.5294    0.8078    0.9804
    1.0000    0.4000         0
    0.8000    0.8000    1.0000
    0.5294    0.8078    0.9804
    1.0000    0.6000    0.2000];
CList=[0.4941    0.5490    0.4118
    0.9059    0.6510    0.3333
    0.8980    0.6157    0.4980
    0.8902    0.5137    0.4667
    0.4275    0.2824    0.2784];
CList=[0.4314    0.4863    0.7255
    0.4824    0.7373    0.8353
    0.8157    0.8863    0.6863
    0.9608    0.8588    0.6000
    0.9098    0.6118    0.5059
    0.8235    0.5176    0.5529];
CList=[0.4000    0.7725    0.8000
    0.9647    0.8118    0.4431
    0.9725    0.6118    0.4549
    0.8627    0.6902    0.9490
    0.5294    0.7725    0.3725
    0.6196    0.7255    0.9529
    0.9961    0.5333    0.6941
    0.7882    0.8588    0.4549
    0.5451    0.8784    0.6431
    0.7059    0.5922    0.9059
    0.8275    0.7059    0.5176
    0.7020    0.7020    0.7020];
CList=[0.3059    0.4745    0.5373
    0.6627    0.0039    0.1059
    0.8941    0.6588    0.1490
    0.5020    0.5804    0.3059
    0.8627    0.8392    0.6980];

Complete code (array of starting and ending points)

%@author : slandarer
S=[1 1 1 1 1 6 6 6 6 6 11 11 11];
T=[2 3 4 5 6 7 8 9 10 11 12 13 14];
R=rand(3,14);
% 自定义了点配色RGB 0-1
CList=[0.3686    0.5059    0.6745
    0.5608    0.6588    0.4784
    0.7490    0.3804    0.4157
    0.9059    0.8235    0.0078
    0.4902    0.3255    0.1608
    0.9569    0.5843    0.2196
    0.4000    0.8039    0.6667
    0.8157    0.4392    0.7255
    0.5961    0.9843    0.5961
    0.9882    0.6392    0.7176];

% 使用MATLAB自带函数构建网络
fig1=figure();
G=graph(S,T);
GHdl=plot(G,'Layout','force');
X=GHdl.XData;
Y=GHdl.YData;
XY=[X(:),Y(:)];
close(fig1)

% 新图窗创建及坐标区域修饰
fig2=figure('Units','normalized','Position',[.2,.2,.4,.6]);
ax=gca;
ax.DataAspectRatio=[1,1,1];
ax.XColor='none';
ax.YColor='none';
L=pdist2(XY,XY);
L(~~eye(size(L,1)))=inf;
L=min(min(L)).*.3;

% 重绘网络图
hold on
LX=[X(S);X(T);S.*nan];
LY=[Y(S);Y(T);S.*nan];
plot(LX(:),LY(:),'LineWidth',1,'Color','k');

% 绘制饼图
R=R./sum(R,1);
Theta=cumsum([zeros(1,size(R,2));R]).*2.*pi;
Tt01=linspace(0,1,50);
for i=1:size(R,2)
    for k=1:size(R,1)
        Tt=(Theta(k+1,i)-Theta(k,i)).*Tt01+Theta(k,i);
        PHdl=fill([X(i),cos(Tt).*L+X(i)],[Y(i),sin(Tt).*L+Y(i)],CList(k,:),'EdgeColor','w','LineWidth',1);
        if i==1,PltHdl(k)=PHdl;end
    end
end

% 绘制图例
lgdHdl=legend(PltHdl,'Box','off','FontName','Times New Roman',...
    'FontSize',13,'Orientation','horizontal','Location','best');
lgdHdl.ItemTokenSize=[14,14];

Complete code (adjacency matrix)

After using the graph function to create an object, you can directly obtain its Edges.EndNodes property as Sa Tmatrix. I believe that smart people should be able to understand it~:

% 随机生成邻接矩阵
A=rand(16)>.8;
A=(A+A')./2;
A(~~eye(size(A)))=0;
R=rand(3,16);
% 自定义了点配色RGB 0-1
CList=[0.3686    0.5059    0.6745
    0.5608    0.6588    0.4784
    0.7490    0.3804    0.4157
    0.9059    0.8235    0.0078
    0.4902    0.3255    0.1608
    0.9569    0.5843    0.2196
    0.4000    0.8039    0.6667
    0.8157    0.4392    0.7255
    0.5961    0.9843    0.5961
    0.9882    0.6392    0.7176];
% 使用MATLAB自带函数构建网络
fig1=figure();
G=graph(A);
GHdl=plot(G,'Layout','circle','Center',1);
S=G.Edges.EndNodes(:,1).';
T=G.Edges.EndNodes(:,2).';
X=GHdl.XData;
Y=GHdl.YData;
XY=[X(:),Y(:)];
close(fig1)

% 新图窗创建及坐标区域修饰
fig2=figure('Units','normalized','Position',[.2,.2,.4,.6]);
ax=gca;
ax.DataAspectRatio=[1,1,1];
ax.XColor='none';
ax.YColor='none';
L=pdist2(XY,XY);
L(~~eye(size(L,1)))=inf;
L=min(min(L)).*.3;

% 重绘网络图
hold on
LX=[X(S);X(T);S.*nan];
LY=[Y(S);Y(T);S.*nan];
plot(LX(:),LY(:),'LineWidth',1,'Color','k');

% 绘制饼图
R=R./sum(R,1);
Theta=cumsum([zeros(1,size(R,2));R]).*2.*pi;
Tt01=linspace(0,1,50);
for i=1:size(R,2)
    for k=1:size(R,1)
        Tt=(Theta(k+1,i)-Theta(k,i)).*Tt01+Theta(k,i);
        PHdl=fill([X(i),cos(Tt).*L+X(i)],[Y(i),sin(Tt).*L+Y(i)],CList(k,:),'EdgeColor','w','LineWidth',1);
        if i==1,PltHdl(k)=PHdl;end
    end
end

% 绘制图例
lgdHdl=legend(PltHdl,'Box','off','FontName','Times New Roman',...
    'FontSize',13,'Orientation','horizontal','Location','best');
lgdHdl.ItemTokenSize=[14,14];