嘿大家好久不见，今天来画一个弧长链接图，大概长这样：
感觉有点像弦图把原本环绕的节点有序的放在了一条直线上：
能够明显的看出弧长链接图更加重视了节点之间的顺序，常见的用法比如：
- 使用节点表示一辆列车各个站点，两个站点之间的连线宽度代表有多少人前一个站点上车，后一个站点下车。
- 人物关系网络，将人物按照首次出场顺序排列。
- 将基因按照其在染色体上的物理位置排列成一条线。如果两个基因在功能上相关或同时被表达（共表达），就用一条弧线将它们连接起来。
代码获取
工具函数完整代码见文末或者gitee仓库：
示例
基本使用
假设我们有一个上三角矩阵，第i行第j列的数值代表由节点i流向节点j的流量，主对角线的数值可以都设置为1，或者用来存储其他可视化信息，用来控制节点大小：
matlab
Data = [25, 0, 11, 22, 24, 25, 8, 0;
0, 14, 0, 0, 0, 0, 4, 0;
0, 0, 11, 0, 0, 0, 0, 0;
0, 0, 0, 22, 0, 20, 17, 0;
0, 0, 0, 0, 24, 3, 6, 3;
0, 0, 0, 0, 0, 25, 7, 0;
0, 0, 0, 0, 0, 0, 17, 0;
0, 0, 0, 0, 0, 0, 0, 11];
% 创建弧长链接图对象(Create a arc chart object)
ARC = arcChart(Data);
% 开始绘图(Start drawing)
ARC.draw();
% 显示并修改标签字体(Show labels and set the font)
ARC.setLabel('FontSize', 17, 'FontName', 'Times New Roman')
% 显示图例(Display legend)
% ARC.nodeLegend()
% ARC.edgeLegend()
% Position
ARC.nodeLegend([-.5, 0], 'FontSize', 15, 'FontName', 'Times New Roman')
ARC.edgeLegend([-.5, 2.5], 'FontSize', 15, 'FontName', 'Times New Roman')
节点大小与线条粗细
节点大小和线条粗细都是一个含两个元素的数组，如果两个元素设置的一样的话，所有节点都一样大，所有弦图都一样粗细：
matlab
Data = [1, 1, 6, 0;
0, 1, 0, 1;
0, 0, 5, 2;
0, 0, 0, 1];
ARC = arcChart(Data);
ARC.NodeName = {'北京','上海','广州','深圳'}; % 设置节点名称(Set node names)
ARC.NodeSizeLim = [.07, .07]; % 设置节点大小范围(Set size limit of node)
ARC.EdgeWidthLim = [.1, .1]; % 设置链接宽度范围(Set width limit of edge)
ARC.draw();
ARC.setLabel()
顺带一提：字体可以单独修改，例如：
matlab
ARC.setLabelN(2, 'Rotation', 0, 'Color','r', 'HorizontalAlignment','center')
链接的渲染
设置RenderingMethod属性即可，可以选择的方法有：
'simple', 'left', 'right', 'interp', 'map', 'bicolor', 'source', 'target'
matlab
rng(1)
Data = randi([1, 25], [8, 8]);
Data(rand([8, 8]) < .65) = 0;
Data = Data + eye(8);
% Color list
CList = [ 75,146,241; 252,180, 65; 224, 64, 10; 5,100,146; 191,191,191;
26, 59,105; 255,227,130; 18,156,221; 202,107, 75; 0, 92,219;
243,210,136; 80, 99,129; 241,185,168; 224,131, 10; 120,147,190]./255;
ARC = arcChart(Data);
% 设置节点和链接颜色，若未设置链接颜色则默认与节点颜色相同
% Set node color and edge color, the default edge color is as same as node color
ARC.NodeColor = CList;
ARC.EdgeColor = CList;
ARC.NodeSizeLim = [.2, .2];
ARC.EdgeWidthLim = [.02, .2];
% 设置链接样式(Set the rendering method for edges)
% 'simple', 'left', 'right', 'interp', 'map', 'bicolor', 'source', 'target'
method = 'target';
ARC.RenderingMethod = method;
ARC.draw();
% colorbar
text(4.5, 4, method, 'FontSize',27, 'FontWeight','bold', 'HorizontalAlignment','center')单色
双色
与左节点颜色相同
与右节点颜色相同
渐变
与数值大小相关
与起始节点颜色相同
与结束节点颜色相同
一个例子
matlab
rng(2)
% 随机生成数据(Randomly generated data)
Data = zeros(40, 40);
Data(1:15, 1:15) = triu(rand(15));
Data(16:20, 16:20) = triu(rand(5));
Data(21:30, 21:30) = triu(rand(10));
Data(31:40, 31:40) = triu(rand(10));
Data(rand([40, 40]) < .65) = 0;
Data = Data + eye(40);
% Colors and name list for nodes
CList = [ 75,146,241; 252,180, 65; 224, 64, 10; 5,100,146]./255;
Class = [ones(1,15), 2.*ones(1,5), 3.*ones(1,10), 4.*ones(1,10)];
NList = [compose('nodeS-%d',1:15), compose('nodeL-%d',1:5), ...
compose('nodeA-%d',1:10), compose('nodeN-%d',1:10)];
ARC = arcChart(Data);
ARC.NodeName = NList;
ARC.NodeColor = CList(Class.',:);
ARC.EdgeColor = [0,0,0];
ARC.NodeSizeLim = [.15,.15];
ARC.EdgeWidthLim = [.01,.06];
ARC.draw();
ARC.setLabel('FontSize',14, 'FontName','Times New Roman')
axis tight
工具函数完整代码：
matlab
classdef arcChart < handle
properties
ax
arginList = {'RenderingMethod', 'NodeSizeLim', 'EdgeWidthLim', ...
'NodeColor', 'EdgeColor'}
dataMat % 数值矩阵
NodeName = {}
NodeColor = [0, 0, 0] % 节点配色
EdgeColor = 'flat' % 链接配色
NodeAlpha = 1 % 节点透明度
EdgeAlpha = .3 % 连接透明度
RenderingMethod = 'simple' % 'left'/'right'/'interp'/'map'
% 'simple'/'bicolor'/'source'/'target'
NodeSizeLim = [.1, .2 ] % 节点大小范围
EdgeWidthLim = [.02, .1] % 链接宽度范围
edgeMatHdl
nodeHdl
labelHdl
end
methods
function obj = arcChart(varargin)
if isa(varargin{1},'matlab.graphics.axis.Axes')
obj.ax = varargin{1};
varargin(1) = [];
else
obj.ax = gca;
end
obj.dataMat = abs(varargin{1});
varargin(1) = [];
for i = 1:2:(length(varargin) - 1)
tid = ismember(lower(obj.arginList), lower(varargin{i}));
if any(tid)
obj.(obj.arginList{tid}) = varargin{i + 1};
end
end
if isempty(obj.NodeName)
obj.NodeName = compose('Node-%d', 1:size(obj.dataMat, 1));
end
end
function obj = draw(obj)
if isstring(obj.EdgeColor) || ischar(obj.EdgeColor)
tmpColor = obj.NodeColor;
else
tmpColor = obj.EdgeColor;
end
% ---------------------------------
obj.ax.NextPlot = 'add';
obj.ax.DataAspectRatio = [1, 1, 1];
obj.ax.XColor = 'none';
obj.ax.YColor = 'none';
% ---------------------------------
t1 = linspace(0, 2*pi, 200);
t2 = linspace(pi, 0, 200);
x1 = cos(t1); y1 = sin(t1);
x2 = cos(t2); y2 = sin(t2);
minN = min(obj.dataMat(eye(size(obj.dataMat)) == 1 & obj.dataMat ~= 0));
maxN = max(obj.dataMat(eye(size(obj.dataMat)) == 1 & obj.dataMat ~= 0));
minE = min(obj.dataMat(eye(size(obj.dataMat)) == 0 & obj.dataMat ~= 0));
maxE = max(obj.dataMat(eye(size(obj.dataMat)) == 0 & obj.dataMat ~= 0));
% 绘制连接
for i = 1:size(obj.dataMat, 1)
for j = 1:size(obj.dataMat, 1)
if i ~= j && obj.dataMat(i, j) ~= 0
if maxE == minE
tR2 = 0*(obj.dataMat(i, j) == 0) + max(abs(obj.EdgeWidthLim))*(obj.dataMat(i, j) > 0);
else
tR2 = 0*(obj.dataMat(i, j) == 0) + ...
((obj.dataMat(i, j) - minE)./(maxE - minE).*abs(diff(obj.EdgeWidthLim)) + min(abs(obj.EdgeWidthLim)))*(obj.dataMat(i, j) > 0);
end
if j > i
tX1 = (i + j)/2 + ((j - i)/2 + tR2)*(x2);
tX2 = (i + j)/2 + ((j - i)/2 - tR2)*x2(end:-1:1);
tY1 = ((j - i)/2 + tR2)*y2;
tY2 = ((j - i)/2 - tR2)*y2(end:-1:1);
else
tX1 = (i + j)/2 + ((i - j)/2 + tR2)*(x2);
tX2 = (i + j)/2 + ((i - j)/2 - tR2)*x2(end:-1:1);
tY1 = - ((i - j)/2 + tR2)*y2;
tY2 = - ((i - j)/2 - tR2)*y2(end:-1:1);
end
TT = repmat(linspace(0,1,10).', [1, 200]);
XX = repmat(tX2(end:-1:1) - tX1, [10, 1]).*TT + repmat(tX1, [10,1]);
YY = repmat(tY2(end:-1:1) - tY1, [10, 1]).*TT + repmat(tY1, [10,1]);
MC = ones(10, 200, 3);
switch obj.RenderingMethod
case 'simple'
obj.edgeMatHdl(i, j) = fill(obj.ax, [tX1, tX2], [tY1, tY2], tmpColor(1, :), 'EdgeColor','none', 'FaceAlpha',obj.EdgeAlpha);
case 'source'
obj.edgeMatHdl(i, j) = fill(obj.ax, [tX1, tX2], [tY1, tY2], tmpColor(mod(i - 1, size(tmpColor, 1)) + 1, :), 'EdgeColor','none', 'FaceAlpha',obj.EdgeAlpha);
case 'target'
obj.edgeMatHdl(i, j) = fill(obj.ax, [tX1, tX2], [tY1, tY2], tmpColor(mod(j - 1, size(tmpColor, 1)) + 1, :), 'EdgeColor','none', 'FaceAlpha',obj.EdgeAlpha);
case 'left'
obj.edgeMatHdl(i, j) = fill(obj.ax, [tX1, tX2], [tY1, tY2], tmpColor(mod(i*(j > i) + j*(j < i) - 1, size(tmpColor, 1)) + 1, :), 'EdgeColor','none', 'FaceAlpha',obj.EdgeAlpha);
case 'right'
obj.edgeMatHdl(i, j) = fill(obj.ax, [tX1, tX2], [tY1, tY2], tmpColor(mod(j*(j > i) + i*(j < i) - 1, size(tmpColor, 1)) + 1, :), 'EdgeColor','none', 'FaceAlpha',obj.EdgeAlpha);
case 'interp'
if j > i
tCi = tmpColor(mod(i - 1, size(tmpColor, 1)) + 1, :);
tCj = tmpColor(mod(j - 1, size(tmpColor, 1)) + 1, :);
else
tCi = tmpColor(mod(j - 1, size(tmpColor, 1)) + 1, :);
tCj = tmpColor(mod(i - 1, size(tmpColor, 1)) + 1, :);
end
MC(:, :, 1) = repmat(linspace(tCi(1), tCj(1), 200), [10, 1]);
MC(:, :, 2) = repmat(linspace(tCi(2), tCj(2), 200), [10, 1]);
MC(:, :, 3) = repmat(linspace(tCi(3), tCj(3), 200), [10, 1]);
obj.edgeMatHdl(i, j) = surf(obj.ax, XX, YY, XX.*0, 'CData',MC, 'EdgeColor','none', 'FaceAlpha',obj.EdgeAlpha);
case 'bicolor'
if j > i
tCi = tmpColor(mod(1 - 1, size(tmpColor, 1)) + 1, :);
tCj = tmpColor(mod(2 - 1, size(tmpColor, 1)) + 1, :);
else
tCi = tmpColor(mod(2 - 1, size(tmpColor, 1)) + 1, :);
tCj = tmpColor(mod(1 - 1, size(tmpColor, 1)) + 1, :);
end
MC(:, :, 1) = repmat(linspace(tCi(1), tCj(1), 200), [10, 1]);
MC(:, :, 2) = repmat(linspace(tCi(2), tCj(2), 200), [10, 1]);
MC(:, :, 3) = repmat(linspace(tCi(3), tCj(3), 200), [10, 1]);
obj.edgeMatHdl(i, j) = surf(obj.ax, XX, YY, XX.*0, 'CData',MC, 'EdgeColor','none', 'FaceAlpha',obj.EdgeAlpha);
case 'map'
obj.edgeMatHdl(i, j) = fill(obj.ax, [tX1, tX2], [tY1, tY2], [0,0,0], 'EdgeColor','none', 'FaceAlpha',obj.EdgeAlpha, 'FaceColor','flat', 'CData',obj.dataMat(i,j));
end
% if obj.dataMat(i, j) == 0
% set(obj.edgeMatHdl(i, j), 'Visible', 'off')
% end
end
end
end
% 绘制节点和标签
for i = 1:size(obj.dataMat, 1)
if maxN == minN
tR1 = 0*(obj.dataMat(i, i) == 0) + max(abs(obj.NodeSizeLim))*(obj.dataMat(i, i) > 0);
else
tR1 = 0*(obj.dataMat(i, i) == 0) + ...
((obj.dataMat(i, i) - minN)./(maxN - minN).*abs(diff(obj.NodeSizeLim)) + min(abs(obj.NodeSizeLim)))*(obj.dataMat(i, i) > 0);
end
obj.nodeHdl(i) = fill(obj.ax, i + x1.*tR1, y1.*tR1, obj.NodeColor(mod(i - 1, size(obj.NodeColor, 1)) + 1, :), ...
'EdgeColor','none', 'FaceAlpha',obj.NodeAlpha);
obj.labelHdl(i) = text(obj.ax, i, -.3, obj.NodeName{i}, 'FontSize',17, 'HorizontalAlignment','right', 'Rotation',45, 'Visible','off');
end
end
function setLabelN(obj, n, varargin)
set(obj.labelHdl(n), 'Visible','on', varargin{:})
end
function setLabel(obj, varargin)
for i = 1:size(obj.dataMat, 1)
set(obj.labelHdl(i), 'Visible','on', varargin{:})
end
end
function nodeLegend(obj, varargin)
if nargin < 2
pos = [-.5, 0];
elseif isnumeric(varargin{1})
pos = varargin{1};
varargin(1) = [];
end
t1 = linspace(0, 2*pi, 200);
x1 = cos(t1); y1 = sin(t1);
minN = min(obj.dataMat(eye(size(obj.dataMat)) == 1 & obj.dataMat ~= 0));
maxN = max(obj.dataMat(eye(size(obj.dataMat)) == 1 & obj.dataMat ~= 0));
fill(obj.ax, x1.*min(abs(obj.NodeSizeLim)) + pos(1), y1.*min(abs(obj.NodeSizeLim)) + pos(2), [1,1,1],'EdgeColor','k','LineWidth',1)
fill(obj.ax, x1.*mean(abs(obj.NodeSizeLim)) + pos(1), y1.*mean(abs(obj.NodeSizeLim)) + pos(2) + 2*sum(abs(obj.NodeSizeLim)), [1,1,1],'EdgeColor','k','LineWidth',1)
fill(obj.ax, x1.*max(abs(obj.NodeSizeLim)) + pos(1), y1.*max(abs(obj.NodeSizeLim)) + pos(2) + 4*sum(abs(obj.NodeSizeLim)), [1,1,1],'EdgeColor','k','LineWidth',1)
plot(obj.ax, pos(1) + max(abs(obj.NodeSizeLim)) + [.1,.1], pos(2) + [0, 4*sum(abs(obj.NodeSizeLim))], 'LineWidth',1, 'Color','k')
plot(obj.ax, pos(1) + max(abs(obj.NodeSizeLim)) + [.1,.2], pos(2) + [0, 0], 'LineWidth',1, 'Color','k')
plot(obj.ax, pos(1) + max(abs(obj.NodeSizeLim)) + [.1,.2], pos(2) + [0, 0] + 4*sum(abs(obj.NodeSizeLim)), 'LineWidth',1, 'Color','k')
text(obj.ax, pos(1) + max(abs(obj.NodeSizeLim)) + .22, pos(2) + 0, num2str(minN), 'FontSize',14,varargin{:})
text(obj.ax, pos(1) + max(abs(obj.NodeSizeLim)) + .22, pos(2) + 4*sum(abs(obj.NodeSizeLim)), num2str(maxN), 'FontSize',14,varargin{:})
end
function edgeLegend(obj, varargin)
if nargin < 2
pos = [-.5, size(obj.dataMat, 1)/2 *.5];
elseif isnumeric(varargin{1})
pos = varargin{1};
varargin(1) = [];
end
x2 = [-1, -1, 1, 1];
y2 = [-1, 1, 1, -1];
minE = min(obj.dataMat(eye(size(obj.dataMat)) == 0 & obj.dataMat ~= 0));
maxE = max(obj.dataMat(eye(size(obj.dataMat)) == 0 & obj.dataMat ~= 0));
fill(obj.ax, x2.*min(abs(obj.EdgeWidthLim)) + pos(1), y2.*min(abs(obj.EdgeWidthLim)) + pos(2), [1,1,1],'EdgeColor','k','LineWidth',1)
fill(obj.ax, x2.*mean(abs(obj.EdgeWidthLim)) + pos(1), y2.*mean(abs(obj.EdgeWidthLim)) + pos(2) + 2*sum(abs(obj.EdgeWidthLim)), [1,1,1],'EdgeColor','k','LineWidth',1)
fill(obj.ax, x2.*max(abs(obj.EdgeWidthLim)) + pos(1), y2.*max(abs(obj.EdgeWidthLim)) + pos(2) + 4*sum(abs(obj.EdgeWidthLim)), [1,1,1],'EdgeColor','k','LineWidth',1)
plot(obj.ax, pos(1) + max(abs(obj.EdgeWidthLim)) + [.1,.1], pos(2) + [0, 4*sum(abs(obj.EdgeWidthLim))], 'LineWidth',1, 'Color','k')
plot(obj.ax, pos(1) + max(abs(obj.EdgeWidthLim)) + [.1,.2], pos(2) + [0, 0], 'LineWidth',1, 'Color','k')
plot(obj.ax, pos(1) + max(abs(obj.EdgeWidthLim)) + [.1,.2], pos(2) + [0, 0] + 4*sum(abs(obj.EdgeWidthLim)), 'LineWidth',1, 'Color','k')
text(obj.ax, pos(1) + max(abs(obj.EdgeWidthLim)) + .22, pos(2) + 0, num2str(minE), 'FontSize',14,varargin{:})
text(obj.ax, pos(1) + max(abs(obj.EdgeWidthLim)) + .22, pos(2) + 4*sum(abs(obj.EdgeWidthLim)), num2str(maxE), 'FontSize',14,varargin{:})
end
end
end