mirror of
https://github.com/MartinThoma/LaTeX-examples.git
synced 2025-04-19 11:38:05 +02:00
(V, E) -> (E, K); added two examples; removed crap
This commit is contained in:
Martin Thoma
parent
71f296ac0b
commit
7253de8aba
11 changed files with 88 additions and 640 deletions
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@ -1,27 +0,0 @@
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#inner-details {
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font-size:12px;
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}
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span.close {
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color:#FF5555;
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cursor:pointer;
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font-weight:bold;
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margin-left:3px;
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}
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span.name {
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cursor: pointer;
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}
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/*TOOLTIPS*/
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.tip {
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text-align: left;
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width:auto;
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max-width:500px;
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||||
}
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.tip-title {
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font-size: 11px;
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text-align:center;
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margin-bottom:2px;
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}
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@ -1,123 +0,0 @@
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html, body {
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margin:0;
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padding:0;
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font-family: "Lucida Grande", Verdana;
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font-size: 0.9em;
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text-align: center;
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background-color:#F2F2F2;
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}
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input, select {
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font-size:0.9em;
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}
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table {
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margin-top:-10px;
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margin-left:7px;
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}
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h4 {
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font-size:1.1em;
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text-decoration:none;
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font-weight:normal;
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color:#23A4FF;
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}
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a {
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color:#23A4FF;
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}
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#container {
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width: 1000px;
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height: 600px;
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margin:0 auto;
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position:relative;
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}
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#left-container,
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#right-container,
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#center-container {
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height:600px;
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position:absolute;
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top:0;
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}
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#left-container, #right-container {
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width:200px;
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color:#686c70;
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text-align: left;
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overflow: auto;
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background-color:#fff;
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background-repeat:no-repeat;
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border-bottom:1px solid #ddd;
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}
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#left-container {
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left:0;
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background-image:url('col2.png');
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background-position:center right;
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border-left:1px solid #ddd;
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}
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#right-container {
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right:0;
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background-image:url('col1.png');
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background-position:center left;
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border-right:1px solid #ddd;
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}
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#right-container h4{
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text-indent:8px;
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}
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#center-container {
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width:600px;
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left:200px;
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background-color:#1a1a1a;
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color:#ccc;
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}
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.text {
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margin: 7px;
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}
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#inner-details {
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font-size:0.8em;
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list-style:none;
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margin:7px;
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}
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#log {
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position:absolute;
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top:10px;
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font-size:1.0em;
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font-weight:bold;
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color:#23A4FF;
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}
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#infovis {
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position:relative;
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width:600px;
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height:600px;
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margin:auto;
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overflow:hidden;
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}
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/*TOOLTIPS*/
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.tip {
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color: #111;
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width: 139px;
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background-color: white;
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border:1px solid #ccc;
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-moz-box-shadow:#555 2px 2px 8px;
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-webkit-box-shadow:#555 2px 2px 8px;
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-o-box-shadow:#555 2px 2px 8px;
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box-shadow:#555 2px 2px 8px;
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opacity:0.9;
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filter:alpha(opacity=90);
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font-size:10px;
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font-family:Verdana, Geneva, Arial, Helvetica, sans-serif;
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padding:7px;
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}
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@ -1,458 +0,0 @@
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var labelType, useGradients, nativeTextSupport, animate;
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(function() {
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var ua = navigator.userAgent,
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iStuff = ua.match(/iPhone/i) || ua.match(/iPad/i),
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typeOfCanvas = typeof HTMLCanvasElement,
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nativeCanvasSupport = (typeOfCanvas == 'object' || typeOfCanvas == 'function'),
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textSupport = nativeCanvasSupport
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&& (typeof document.createElement('canvas').getContext('2d').fillText == 'function');
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//I'm setting this based on the fact that ExCanvas provides text support for IE
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//and that as of today iPhone/iPad current text support is lame
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labelType = (!nativeCanvasSupport || (textSupport && !iStuff))? 'Native' : 'HTML';
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nativeTextSupport = labelType == 'Native';
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useGradients = nativeCanvasSupport;
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animate = !(iStuff || !nativeCanvasSupport);
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})();
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var Log = {
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elem: false,
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write: function(text){
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if (!this.elem)
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this.elem = document.getElementById('log');
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this.elem.innerHTML = text;
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this.elem.style.left = (500 - this.elem.offsetWidth / 2) + 'px';
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}
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};
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function init(){
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// init data
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var json = [
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{
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"adjacencies": [
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"graphnode0",
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{
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"nodeTo": "graphnode1",
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"nodeFrom": "graphnode0",
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"data": {
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"$color": "#557EAA"
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}
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}, {
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"nodeTo": "graphnode5",
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"nodeFrom": "graphnode0",
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"data": {
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"$color": "#909291"
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}
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}, {
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"nodeTo": "graphnode9",
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"nodeFrom": "graphnode0",
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"data": {
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"$color": "#557EAA"
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}
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}
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],
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"data": {
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"$color": "#83548B",
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"$type": "circle",
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"$dim": 8
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},
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"id": "graphnode0",
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"name": "graphnode0"
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}, {
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"adjacencies": [
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"graphnode1",
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{
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"nodeTo": "graphnode8",
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"nodeFrom": "graphnode1",
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"data": {
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"$color": "#557EAA"
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}
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}, {
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"nodeTo": "graphnode0",
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"nodeFrom": "graphnode1",
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"data": {
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"$color": "#909291"
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}
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}, {
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"nodeTo": "graphnode2",
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"nodeFrom": "graphnode1",
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"data": {
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"$color": "#557EAA"
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}
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}
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],
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"data": {
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"$color": "#83548B",
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"$type": "circle",
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"$dim": 8
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},
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"id": "graphnode1",
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"name": "graphnode1"
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}, {
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"adjacencies": [
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"graphnode2",
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{
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"nodeTo": "graphnode1",
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"nodeFrom": "graphnode2",
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"data": {
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"$color": "#557EAA"
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}
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}, {
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"nodeTo": "graphnode3",
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"nodeFrom": "graphnode2",
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"data": {
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"$color": "#909291"
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}
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}, {
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"nodeTo": "graphnode6",
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"nodeFrom": "graphnode2",
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"data": {
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"$color": "#557EAA"
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}
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}
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],
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"data": {
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"$color": "#83548B",
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"$type": "circle",
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"$dim": 8
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},
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"id": "graphnode2",
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"name": "graphnode2"
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}, {
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"adjacencies": [
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"graphnode3",
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{
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"nodeTo": "graphnode2",
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"nodeFrom": "graphnode3",
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"data": {
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"$color": "#557EAA"
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}
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}, {
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"nodeTo": "graphnode4",
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"nodeFrom": "graphnode3",
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"data": {
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"$color": "#909291"
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}
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}, {
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"nodeTo": "graphnode9",
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"nodeFrom": "graphnode3",
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"data": {
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"$color": "#557EAA"
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}
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}
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],
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"data": {
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"$color": "#83548B",
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"$type": "circle",
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"$dim": 8
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},
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"id": "graphnode3",
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"name": "graphnode3"
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}, {
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"adjacencies": [
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"graphnode4",
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{
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"nodeTo": "graphnode3",
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"nodeFrom": "graphnode4",
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"data": {
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"$color": "#557EAA"
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}
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}, {
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"nodeTo": "graphnode5",
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"nodeFrom": "graphnode4",
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"data": {
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"$color": "#909291"
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}
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}, {
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"nodeTo": "graphnode8",
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"nodeFrom": "graphnode4",
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"data": {
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"$color": "#557EAA"
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}
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}
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],
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"data": {
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"$color": "#83548B",
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"$type": "circle",
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"$dim": 8
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},
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"id": "graphnode4",
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"name": "graphnode4"
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}, {
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"adjacencies": [
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"graphnode5",
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{
|
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"nodeTo": "graphnode4",
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"nodeFrom": "graphnode5",
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"data": {
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"$color": "#557EAA"
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}
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}, {
|
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"nodeTo": "graphnode0",
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"nodeFrom": "graphnode5",
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"data": {
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"$color": "#909291"
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}
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}, {
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"nodeTo": "graphnode6",
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"nodeFrom": "graphnode5",
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"data": {
|
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"$color": "#557EAA"
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}
|
||||
}
|
||||
],
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"data": {
|
||||
"$color": "#83548B",
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"$type": "circle",
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"$dim": 8
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},
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"id": "graphnode5",
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"name": "graphnode5"
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}, {
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"adjacencies": [
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"graphnode6",
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{
|
||||
"nodeTo": "graphnode5",
|
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"nodeFrom": "graphnode6",
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"data": {
|
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"$color": "#557EAA"
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}
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}, {
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"nodeTo": "graphnode2",
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"nodeFrom": "graphnode6",
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"data": {
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"$color": "#909291"
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}
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}, {
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"nodeTo": "graphnode7",
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"nodeFrom": "graphnode6",
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"data": {
|
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"$color": "#557EAA"
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}
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||||
}
|
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],
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"data": {
|
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"$color": "#83548B",
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"$type": "circle",
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"$dim": 8
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},
|
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"id": "graphnode6",
|
||||
"name": "graphnode6"
|
||||
}, {
|
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"adjacencies": [
|
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"graphnode7",
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{
|
||||
"nodeTo": "graphnode6",
|
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"nodeFrom": "graphnode7",
|
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"data": {
|
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"$color": "#557EAA"
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}
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}, {
|
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"nodeTo": "graphnode8",
|
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"nodeFrom": "graphnode7",
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"data": {
|
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"$color": "#909291"
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}
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}, {
|
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"nodeTo": "graphnode9",
|
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"nodeFrom": "graphnode7",
|
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"data": {
|
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"$color": "#557EAA"
|
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}
|
||||
}
|
||||
],
|
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"data": {
|
||||
"$color": "#83548B",
|
||||
"$type": "circle",
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"$dim": 8
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},
|
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"id": "graphnode7",
|
||||
"name": "graphnode7"
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}, {
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"adjacencies": [
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"graphnode8",
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{
|
||||
"nodeTo": "graphnode1",
|
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"nodeFrom": "graphnode8",
|
||||
"data": {
|
||||
"$color": "#557EAA"
|
||||
}
|
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}, {
|
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"nodeTo": "graphnode4",
|
||||
"nodeFrom": "graphnode8",
|
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"data": {
|
||||
"$color": "#909291"
|
||||
}
|
||||
}, {
|
||||
"nodeTo": "graphnode7",
|
||||
"nodeFrom": "graphnode8",
|
||||
"data": {
|
||||
"$color": "#557EAA"
|
||||
}
|
||||
}
|
||||
],
|
||||
"data": {
|
||||
"$color": "#83548B",
|
||||
"$type": "circle",
|
||||
"$dim": 8
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||||
},
|
||||
"id": "graphnode8",
|
||||
"name": "graphnode8"
|
||||
}, {
|
||||
"adjacencies": [
|
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"graphnode9",
|
||||
{
|
||||
"nodeTo": "graphnode0",
|
||||
"nodeFrom": "graphnode9",
|
||||
"data": {
|
||||
"$color": "#557EAA"
|
||||
}
|
||||
}, {
|
||||
"nodeTo": "graphnode3",
|
||||
"nodeFrom": "graphnode9",
|
||||
"data": {
|
||||
"$color": "#909291"
|
||||
}
|
||||
}, {
|
||||
"nodeTo": "graphnode7",
|
||||
"nodeFrom": "graphnode9",
|
||||
"data": {
|
||||
"$color": "#557EAA"
|
||||
}
|
||||
}
|
||||
],
|
||||
"data": {
|
||||
"$color": "#83548B",
|
||||
"$type": "circle",
|
||||
"$dim": 8
|
||||
},
|
||||
"id": "graphnode9",
|
||||
"name": "graphnode9"
|
||||
}
|
||||
];
|
||||
// end
|
||||
// init ForceDirected
|
||||
var fd = new $jit.ForceDirected({
|
||||
//id of the visualization container
|
||||
injectInto: 'infovis',
|
||||
//Enable zooming and panning
|
||||
//by scrolling and DnD
|
||||
Navigation: {
|
||||
enable: true,
|
||||
//Enable panning events only if we're dragging the empty
|
||||
//canvas (and not a node).
|
||||
panning: 'avoid nodes',
|
||||
zooming: 10 //zoom speed. higher is more sensible
|
||||
},
|
||||
// Change node and edge styles such as
|
||||
// color and width.
|
||||
// These properties are also set per node
|
||||
// with dollar prefixed data-properties in the
|
||||
// JSON structure.
|
||||
Node: {
|
||||
overridable: true
|
||||
},
|
||||
Edge: {
|
||||
overridable: true,
|
||||
color: '#23A4FF',
|
||||
lineWidth: 0.4
|
||||
},
|
||||
//Native canvas text styling
|
||||
Label: {
|
||||
type: labelType, //Native or HTML
|
||||
size: 10,
|
||||
style: 'bold'
|
||||
},
|
||||
//Add Tips
|
||||
Tips: {
|
||||
enable: true,
|
||||
onShow: function(tip, node) {
|
||||
//count connections
|
||||
var count = 0;
|
||||
node.eachAdjacency(function() { count++; });
|
||||
//display node info in tooltip
|
||||
tip.innerHTML = "<div class=\"tip-title\">" + node.name + "</div>"
|
||||
+ "<div class=\"tip-text\"><b>connections:</b> " + count + "</div>";
|
||||
}
|
||||
},
|
||||
// Add node events
|
||||
Events: {
|
||||
enable: true,
|
||||
type: 'Native',
|
||||
//Change cursor style when hovering a node
|
||||
onMouseEnter: function() {
|
||||
fd.canvas.getElement().style.cursor = 'move';
|
||||
},
|
||||
onMouseLeave: function() {
|
||||
fd.canvas.getElement().style.cursor = '';
|
||||
},
|
||||
//Update node positions when dragged
|
||||
onDragMove: function(node, eventInfo, e) {
|
||||
var pos = eventInfo.getPos();
|
||||
node.pos.setc(pos.x, pos.y);
|
||||
fd.plot();
|
||||
},
|
||||
//Implement the same handler for touchscreens
|
||||
onTouchMove: function(node, eventInfo, e) {
|
||||
$jit.util.event.stop(e); //stop default touchmove event
|
||||
this.onDragMove(node, eventInfo, e);
|
||||
},
|
||||
//Add also a click handler to nodes
|
||||
onClick: function(node) {
|
||||
if(!node) return;
|
||||
// Build the right column relations list.
|
||||
// This is done by traversing the clicked node connections.
|
||||
var html = "<h4>" + node.name + "</h4><b> connections:</b><ul><li>",
|
||||
list = [];
|
||||
node.eachAdjacency(function(adj){
|
||||
list.push(adj.nodeTo.name);
|
||||
});
|
||||
//append connections information
|
||||
$jit.id('inner-details').innerHTML = html + list.join("</li><li>") + "</li></ul>";
|
||||
}
|
||||
},
|
||||
//Number of iterations for the FD algorithm
|
||||
iterations: 200,
|
||||
//Edge length
|
||||
levelDistance: 130,
|
||||
// Add text to the labels. This method is only triggered
|
||||
// on label creation and only for DOM labels (not native canvas ones).
|
||||
onCreateLabel: function(domElement, node){
|
||||
domElement.innerHTML = node.name;
|
||||
var style = domElement.style;
|
||||
style.fontSize = "0.8em";
|
||||
style.color = "#ddd";
|
||||
},
|
||||
// Change node styles when DOM labels are placed
|
||||
// or moved.
|
||||
onPlaceLabel: function(domElement, node){
|
||||
var style = domElement.style;
|
||||
var left = parseInt(style.left);
|
||||
var top = parseInt(style.top);
|
||||
var w = domElement.offsetWidth;
|
||||
style.left = (left - w / 2) + 'px';
|
||||
style.top = (top + 10) + 'px';
|
||||
style.display = '';
|
||||
}
|
||||
});
|
||||
// load JSON data.
|
||||
fd.loadJSON(json);
|
||||
// compute positions incrementally and animate.
|
||||
fd.computeIncremental({
|
||||
iter: 40,
|
||||
property: 'end',
|
||||
onStep: function(perc){
|
||||
Log.write(perc + '% loaded...');
|
||||
},
|
||||
onComplete: function(){
|
||||
Log.write('done');
|
||||
fd.animate({
|
||||
modes: ['linear'],
|
||||
transition: $jit.Trans.Elastic.easeOut,
|
||||
duration: 2500
|
||||
});
|
||||
}
|
||||
});
|
||||
// end
|
||||
}
|
||||
File diff suppressed because one or more lines are too long
Binary file not shown.
|
|
@ -36,7 +36,7 @@ Kantenmenge bezeichnet.
|
|||
|
||||
\begin{frame}{Inzidenz}
|
||||
\begin{block}{Inzidenz}
|
||||
Sei $e \in E$ und $k = \Set{v_1, v_2} \in K$.
|
||||
Sei $e \in E$ und $k = \Set{e_1, e_2} \in K$.
|
||||
|
||||
$e$ heißt \textbf{inzident} zu $k :\Leftrightarrow e = e_1$ oder $e = e_2$
|
||||
\end{block}
|
||||
|
|
|
|||
|
|
@ -30,7 +30,6 @@ Ein Graph heißt \textbf{eulersch}, wenn er einen eulerschen Kreis enthält.
|
|||
\pgfsetlayers{background,main}
|
||||
\begin{frame}{Eulerscher Kreis}
|
||||
\newcommand\n{5}
|
||||
\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]
|
||||
\begin{center}
|
||||
\adjustbox{max size={\textwidth}{0.8\textheight}}{
|
||||
\begin{tikzpicture}
|
||||
|
|
|
|||
|
|
@ -130,9 +130,9 @@ seine \textbf{Länge}.
|
|||
|
||||
\begin{frame}{Geschlossener Kantenzug}
|
||||
\begin{block}{Geschlossener Kantenzug}
|
||||
Sei $G = (V, E)$ ein Graph und $A = (e_1, e_2 \dots, e_s)$ ein Kantenzug.
|
||||
Sei $G = (E, K)$ ein Graph und $A = (e_0, e_1, \dots, e_s)$ ein Kantenzug.
|
||||
|
||||
A heißt \textbf{geschlossen} $:\Leftrightarrow v_s = v_0$ .
|
||||
A heißt \textbf{geschlossen} $:\Leftrightarrow e_s = e_0$ .
|
||||
\end{block}
|
||||
|
||||
\begin{gallery}
|
||||
|
|
@ -149,9 +149,9 @@ A heißt \textbf{geschlossen} $:\Leftrightarrow v_s = v_0$ .
|
|||
|
||||
\begin{frame}{Weg}
|
||||
\begin{block}{Weg}
|
||||
Sei $G = (V, E)$ ein Graph und $A = (e_1, e_2 \dots, e_s)$ ein Kantenzug.
|
||||
Sei $G = (E, K)$ ein Graph und $A = (k_1, k_2 \dots, k_s)$ ein Kantenzug.
|
||||
|
||||
A heißt \textbf{Weg} $:\Leftrightarrow \forall_{i, j \in [1, s] \cap \mathbb{N}}: i \neq j \Rightarrow e_i \neq e_j$ .
|
||||
A heißt \textbf{Weg} $:\Leftrightarrow \forall_{i, j \in 1, \dots, s}: i \neq j \Rightarrow k_i \neq k_j$ .
|
||||
\end{block}
|
||||
|
||||
\pause
|
||||
|
|
@ -167,7 +167,7 @@ Achtung: Knoten dürfen mehrfach abgelaufen werden!
|
|||
|
||||
\begin{frame}{Kreis}
|
||||
\begin{block}{Kreis}
|
||||
Sei $G = (V, E)$ ein Graph und $A = (e_1, e_2 \dots, e_s)$ ein Kantenzug.
|
||||
Sei $G = (E, K)$ ein Graph und $A = (k_1, k_2 \dots, k_s)$ ein Kantenzug.
|
||||
|
||||
A heißt \textbf{Kreis} $:\Leftrightarrow A$ ist geschlossen und ein Weg.
|
||||
\end{block}
|
||||
|
|
@ -175,13 +175,20 @@ A heißt \textbf{Kreis} $:\Leftrightarrow A$ ist geschlossen und ein Weg.
|
|||
\pause
|
||||
|
||||
Manchmal wird das auch "`einfacher Kreis"' genannt.
|
||||
|
||||
\pause
|
||||
|
||||
\begin{gallery}
|
||||
\galleryimage[Green]{graphs/circle-one-facet}
|
||||
\galleryimage[Green]{graphs/circle-two-facets}
|
||||
\end{gallery}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Zusammenhängender Graph}
|
||||
\begin{block}{Zusammenhängender Graph}
|
||||
Sei $G = (V, E)$ ein Graph.
|
||||
Sei $G = (E, K)$ ein Graph.
|
||||
|
||||
$G$ heißt \textbf{zusammenhängend} $:\Leftrightarrow \forall v_1, v_2 \in V: $ Es ex. ein Kantenzug, der $v_1$ und $v_2$ verbindet
|
||||
$G$ heißt \textbf{zusammenhängend} $:\Leftrightarrow \forall e_1, e_2 \in E: $ Es ex. ein Kantenzug, der $e_1$ und $e_2$ verbindet
|
||||
\end{block}
|
||||
|
||||
\begin{gallery}
|
||||
|
|
|
|||
|
|
@ -0,0 +1,36 @@
|
|||
\documentclass[varwidth=true, border=2pt]{standalone}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{arrows,positioning}
|
||||
\tikzset{
|
||||
%Define standard arrow tip
|
||||
>=stealth',
|
||||
% Define arrow style
|
||||
pil/.style={->,thick}
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\node (a)[vertex] at (0,0) {};
|
||||
\node (b)[vertex] at (1,1) {};
|
||||
\node (c)[vertex] at (2,1) {};
|
||||
\node (d)[vertex] at (3,0) {};
|
||||
\node (e)[vertex] at (4,1) {};
|
||||
\node (f)[vertex] at (5,1) {};
|
||||
\node (g)[vertex] at (6,0) {};
|
||||
\node (h)[vertex] at (5,-1) {};
|
||||
\node (i)[vertex] at (4,-1) {};
|
||||
%\node (j)[vertex] at (3,0) {};
|
||||
\node (k)[vertex] at (2,-1) {};
|
||||
\node (l)[vertex] at (1,-1) {};
|
||||
\node (m)[vertex] at (2,2) {};
|
||||
\node (n)[vertex] at (3,2) {};
|
||||
|
||||
\foreach \from/\to in {a/b,b/c,c/d,d/k,k/l,l/a}
|
||||
\draw[selected edge] (\from) -- (\to);
|
||||
|
||||
\foreach \from/\to in {a/b,b/c,c/d,d/e,e/f,f/g,g/h,h/i,i/d,d/k,k/l,l/a}
|
||||
\draw[line width=2pt] (\from) -- (\to);
|
||||
\draw[line width=2pt] (b) -- (m);
|
||||
\draw[line width=2pt] (m) -- (n);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
|
@ -0,0 +1,36 @@
|
|||
\documentclass[varwidth=true, border=2pt]{standalone}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{arrows,positioning}
|
||||
\tikzset{
|
||||
%Define standard arrow tip
|
||||
>=stealth',
|
||||
% Define arrow style
|
||||
pil/.style={->,thick}
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\node (a)[vertex] at (0,0) {};
|
||||
\node (b)[vertex] at (1,1) {};
|
||||
\node (c)[vertex] at (2,1) {};
|
||||
\node (d)[vertex] at (3,0) {};
|
||||
\node (e)[vertex] at (4,1) {};
|
||||
\node (f)[vertex] at (5,1) {};
|
||||
\node (g)[vertex] at (6,0) {};
|
||||
\node (h)[vertex] at (5,-1) {};
|
||||
\node (i)[vertex] at (4,-1) {};
|
||||
%\node (j)[vertex] at (3,0) {};
|
||||
\node (k)[vertex] at (2,-1) {};
|
||||
\node (l)[vertex] at (1,-1) {};
|
||||
\node (m)[vertex] at (2,2) {};
|
||||
\node (n)[vertex] at (3,2) {};
|
||||
|
||||
\foreach \from/\to in {a/b,b/c,c/d,d/e,e/f,f/g,g/h,h/i,i/d,d/k,k/l,l/a}
|
||||
\draw[selected edge] (\from) -- (\to);
|
||||
|
||||
\foreach \from/\to in {a/b,b/c,c/d,d/e,e/f,f/g,g/h,h/i,i/d,d/k,k/l,l/a}
|
||||
\draw[line width=2pt] (\from) -- (\to);
|
||||
\draw[line width=2pt] (b) -- (m);
|
||||
\draw[line width=2pt] (m) -- (n);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
|
@ -132,5 +132,6 @@
|
|||
\definecolor{Green}{HTML}{BEF781}
|
||||
|
||||
\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
|
||||
\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]
|
||||
\def\TCop{\textsuperscript{\textcopyright}} % Copyright-sign
|
||||
\usepackage{mathtools}
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue