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Bigraphs 2019 01 - A Bigraph Relational Model
<?xml version="1.0" encoding="UTF-8"?>
<!--Xholon Workbook http://www.primordion.com/Xholon/gwt/ MIT License, Copyright (C) Ken Webb, Tue Jun 18 2019 17:58:46 GMT-0400 (Eastern Daylight Time)-->
<XholonWorkbook>
<Notes><![CDATA[
Xholon
------
Title: Bigraphs 2019 01 - A Bigraph Relational Model
Description:
Url: http://www.primordion.com/Xholon/gwt/
InternalName: 6882561aa5b59ab93cace22d02840bae
Keywords:
My Notes
--------
June 13, 2019
In this workbook, I explore and implement the bigraph Vending Machine example [1]. See Figure 1 and the bigraph specification on page 16.
I will try to implement the example in Xholon, by taking the following specification[1] as code in a Bigraph Domain Specific Language (DSL).
A bigraph B under a signature Σ is defined as
B=(VB,EB,PB,ctrlB,prntB,linkB):〈m,X〉→〈n,Y〉
Bigraph Specification (with added line numbers)
---------------------
1 Σ=({get,send,sum},{(get,1),(send,1),(sum,0)}),
2 VB={a,b,d,e,f,g,h,i,j,k,l},
3 EB=∅,
4 PB={p(b,1),p(e,1),p(g,1),p(i,1),p(j,1),p(l,1)},
5 ctrlB={(a,sum),(b,send),(d,sum),(e,get),(f,sum),(g,get),(h,sum),(i,send),(j,get),(k,sum),(l,send)},
6 prntB={(a,0),(f,0),(b,a),(d,b),(e,d),(g,f),(h,g),(i,h),(j,f),(k,j),(l,k)},
7 linkB={(p(b,1),c),(p(e,1),co),(p(g,1),c),(p(i,1),co),(p(j,1),c),(p(l,1),t),
8 m=0,X=∅,n=1,and,Y={c,co,t}
-----
Bigraph Specification (details on each line)
---------------------
1 Σ is a signature
2 VB a set of nodes (vertices); note that "k" was missing
3 EB a set of edges
4 PB a set of ports
5 ctrlB a set of controls
6 prntB a set of parent pairs
7 linkB maps links; note the missing "}"
8 note the unnecessary word "and"
-----
TODO
----
- how do I handle inner and outer names?
- perhaps they could be Xholon nodes within an array called outerNames in me or me.parent() ?
- I think these are ROOM/OT/eTrice relay ports
- how do I specify edges in my enhanced bigraph specification?
- an edge is just a label, the name of a hyperedge (see ref[2])
- and see ref[1] page 15-17, especially first para on page 16
- an edge is just an identifier
- also see page 35-36 of ref[1]
- edges become links between ports and outer names
- maybe this has something to do with the fact that a Xholon edge/link can be specified as a path over the place graph (using XPath, etc.)
- and XML and HTML also use XPath
- there needs to a way with bigraphs to specify class inheritance
- probably using something analogous to prntB
graphviz
--------
/*
Automatically generated by Xholon version 0.9.1, using org.primordion.ef.Xholon2Graphviz.java
Fri Jun 14 10:34:57 GMT-400 2019 1560522897863
model: Bigraphs 2019 01 - A Bigraph Relational Model
www.primordion.com/Xholon
To view this file, use Graphviz dot|fdp|neato|twopi|circo|sfdp from http://www.graphviz.org/
For example, to generate an SVG file:
dot -Tsvg -O BigraphSystem_45_1560522897863.gv
Alternatively try one of these:
dot -Tsvg -O BigraphSystem_45_1560522897863.gv
dot -Tsvg -O -Grankdir=LR BigraphSystem_45_1560522897863.gv
fdp -Tsvg -O BigraphSystem_45_1560522897863.gv
neato -Tsvg -O BigraphSystem_45_1560522897863.gv
circo -Tsvg -O BigraphSystem_45_1560522897863.gv
Or use one of: -Tgif -Tjpg -Tpdf -Tpng -Txdot -Txlib
See also: http://www.webgraphviz.com/
See also: http://rise4fun.com/agl/
To repeat this Xholon export:
$wnd.xh.xport("Graphviz", $wnd.xh.root().parent().xpath("Chameleon/BigraphSystem"), '{"gvFileExt":".gv","gvGraph":"digraph","layout":"dot","edgeOp":"->","gvCluster":"cluster","shouldShowStateMachineEntities":false,"filter":"--Behavior,Script","nameTemplateNodeId":"^^^^i^","nameTemplateNodeLabel":"r c^^^","shouldQuoteLabels":true,"shouldShowLinks":true,"shouldShowLinkLabels":false,"shouldSpecifyLayout":false,"maxLabelLen":-1,"shouldColor":true,"defaultNodeColor":"#ffffff","bgGraphColor":"white","shouldSpecifyShape":true,"shape":"box","shouldSpecifySize":true,"size":"22","shouldSpecifyFontname":true,"fontname":"\"Courier New\"","shouldSpecifyArrowhead":false,"arrowhead":"vee","shouldSpecifyStylesheet":true,"stylesheet":"Xholon.css","shouldSpecifyRankdir":true,"rankdir":"TB","shouldDisplayGraph":true,"outputFormat":"svg"}');
*/
digraph 45 {
graph [label="0 bigraphSystem",id="BigraphSystem",stylesheet="Xholon.css",rankdir=TB,size=22,fontname="Courier New",compound=true,bgcolor=white]
node [style=filled,fillcolor="#ffffff",shape=box,fontname="Courier New"]
subgraph cluster51 { label="a sum" id="BigraphSystem/sum[@roleName='a']"
subgraph cluster53 { label="b send" id="BigraphSystem/sum[@roleName='a']/send"
subgraph cluster55 { label="d sum" id="BigraphSystem/sum[@roleName='a']/send/sum"
57 [label="e get" id="BigraphSystem/sum[@roleName='a']/send/sum/get"]
}
}
}
subgraph cluster59 { label="f sum" id="BigraphSystem/sum[@roleName='f']"
subgraph cluster61 { label="g get" id="BigraphSystem/sum[@roleName='f']/get[@roleName='g']"
subgraph cluster63 { label="h sum" id="BigraphSystem/sum[@roleName='f']/get[@roleName='g']/sum"
65 [label="i send" id="BigraphSystem/sum[@roleName='f']/get[@roleName='g']/sum/send"]
}
}
subgraph cluster67 { label="j get" id="BigraphSystem/sum[@roleName='f']/get[@roleName='j']"
subgraph cluster69 { label="k sum" id="BigraphSystem/sum[@roleName='f']/get[@roleName='j']/sum"
71 [label="l send" id="BigraphSystem/sum[@roleName='f']/get[@roleName='j']/sum/send"]
}
}
}
}
export graphviz from Dev Tools
------------------------------
xh.xport("Graphviz", xh.root().parent().xpath("Chameleon/BigraphSystem"), '{"gvFileExt":".gv","gvGraph":"digraph","layout":"dot","edgeOp":"->","gvCluster":"cluster","shouldShowStateMachineEntities":false,"filter":"--Behavior,Script","nameTemplateNodeId":"^^^^i^","nameTemplateNodeLabel":"r c^^^","shouldQuoteLabels":true,"shouldShowLinks":true,"shouldShowLinkLabels":false,"shouldSpecifyLayout":false,"maxLabelLen":-1,"shouldColor":true,"defaultNodeColor":"#ffffff","bgGraphColor":"white","shouldSpecifyShape":true,"shape":"box","shouldSpecifySize":true,"size":"22","shouldSpecifyFontname":true,"fontname":"Courier","shouldSpecifyArrowhead":false,"arrowhead":"vee","shouldSpecifyStylesheet":true,"stylesheet":"Xholon.css","shouldSpecifyRankdir":true,"rankdir":"TB","shouldDisplayGraph":true,"outputFormat":"svg"}');
References
----------
(1) https://arxiv.org/pdf/1111.0086.pdf
A Bigraph Relational Model, by Maxime Beauquier and Carstern Schurmann, IT University of Copenhagen, 2011
(2) BigActors - A Model for Structure-aware Computation, by Eloi Pereira et al, 2013 (page 2)
A bigraph B is called concrete when each node and each edge is assigned a unique identifier (known as support).
We denote the set of node identifiers of B as VB and the set of edge identifiers as EB (e.g. VB = {m0,m1,m2,q0,q1} and EB = {e} in the example of Figure 2).
]]></Notes>
<params>
<param name="MaxPorts" value="5"/>
</params>
<_-.XholonClass>
<BigraphSystem/>
</_-.XholonClass>
<xholonClassDetails>
<Avatar><Color>red</Color></Avatar>
</xholonClassDetails>
<BigraphSystem>
<!-- this is the original specification from ref [1] -->
<Bigraph roleName="0"><Attribute_String><![CDATA[
B=(VB,EB,PB,ctrlB,prntB,linkB):〈m,X〉→〈n,Y〉,
m=0,X=∅,n=1,Y={c,co,t},
Σ=({get,send,sum},{(get,1),(send,1),(sum,0)}),
VB={a,b,d,e,f,g,h,i,j,k,l},
EB=∅,
PB={p(b,1),p(e,1),p(g,1),p(i,1),p(j,1),p(l,1)},
ctrlB={(a,sum),(b,send),(d,sum),(e,get),(f,sum),(g,get),(h,sum),(i,send),(j,get),(k,sum),(l,send)},
prntB={(a,0),(f,0),(b,a),(d,b),(e,d),(g,f),(h,g),(i,h),(j,f),(k,j),(l,k)},
linkB={(p(b,1),c),(p(e,1),co),(p(g,1),c),(p(i,1),co),(p(j,1),c),(p(l,1),t)}
]]></Attribute_String></Bigraph>
<!-- I've added a second linkB, a second PB, and a second EB; and I removed the signature Σ because this has already been defined above -->
<Bigraph roleName="1"><Attribute_String><![CDATA[
B=(VB,EB,PB,ctrlB,prntB,linkB):〈m,X〉→〈n,Y〉,
m=0,X=∅,n=1,Y={c,co,t},
VB={a,b,d,e,f,g,h,i,j,k,l},
EB=∅,
EB={q},
PB={p(b,1),p(e,1),p(g,1),p(i,1),p(j,1),p(l,1)},
PB={p(e,1),p(e,2)},
ctrlB={(a,sum),(b,send),(d,sum),(e,get),(f,sum),(g,get),(h,sum),(i,send),(j,get),(k,sum),(l,send)},
prntB={(a,0),(f,0),(b,a),(d,b),(e,d),(g,f),(h,g),(i,h),(j,f),(k,j),(l,k)},
linkB={(p(b,1),c),(p(e,1),co),(p(g,1),c),(p(i,1),co),(p(j,1),c),(p(l,1),t)},
linkB={(p(e,1),l),(p(e,2),i)}
]]></Attribute_String></Bigraph>
<!-- parse a bigraph(B) interface and signature(Σ) -->
<Bigraph roleName="2"><Attribute_String><![CDATA[
B=(VB,EB,PB,ctrlB,prntB,linkB):〈m,X〉→〈n,Y〉,
m=0,X=∅,n=1,Y={aaa,bbb,ccc},
Σ=({one,two,three},{(one,1),(two,1),(three,0)})
]]></Attribute_String></Bigraph>
<Bigraph roleName="2a"><Attribute_String><![CDATA[
VB={a1,a2,a3,b1,c1,c2},
EB={q,r},
PB={p(a1,1),p(c2,1)},
ctrlB={(a1,one),(a2,two),(a3,three),(b1,one),(c1,one),(c2,two)},
prntB={(a1,0),(a2,a1),(a3,a2),(b1,a1),(c1,a1),(c2,a1)},
linkB={(p(a1,1),c2),(p(c1,1),b1)}
]]></Attribute_String></Bigraph>
<Bigraph roleName="2b"><Attribute_String><![CDATA[
VB={d1,d2,d3,e1,f1,f2},
EB={s,t},
PB={p(d1,1),p(f2,1)},
ctrlB={(d1,one),(d2,two),(d3,three),(e1,one),(f1,one),(f2,two)},
prntB={(d1,0),(d2,d1),(d3,d2),(e1,d1),(f1,d1),(f2,d1)},
linkB={(p(d1,1),f2),(p(f1,1),e1)}
]]></Attribute_String></Bigraph>
<!-- Operand as a Bigraph "Pixel Array 1.1"
pack P' = {}
pack P1 = {w1, x1}
pack P2 = {w2, y2}
cables C = {w, x, y}
bindings w1,w2 |-> w
bindings x1 |-> x
bindings y2 |-> y
morphism (P1, P2) -> P'
- there are many differences between bigraphs and operads, and yet they both handle place graphs and link graphs
-->
<Bigraph roleName="3"><Attribute_String><![CDATA[
B=(VB,EB,PB,ctrlB,prntB,linkB):〈m,X〉→〈n,Y〉,
m=0,X=∅,n=1,Y={c,co,t},
Σ=({P0,P1,P2,C},{(P0,0),(P1,2),(P2,2),(C,0)}),
VB={p0,p1,p2,c},
EB=∅,
PB={p(p1,1),p(p1,2),p(p2,1),p(p2,2),p(c,1),p(c,2),p(c,3)},
ctrlB={(p0,P0),(p1,P1),(p2,P2),(c,C)},
prntB={(p0,0),(p1,p0),(p2,p0)},
linkB={(p(p1,1),c),(p(p1,2)c),(p(p2,1)c),(p(p2,2),c)}
]]></Attribute_String></Bigraph>
</BigraphSystem>
<Bigraphbehavior implName="org.primordion.xholon.base.Behavior_gwtjs"><![CDATA[
const DEFAULT_SITES_SYMBOL = "m";
const DEFAULT_INNERNAMES_SYMBOL = "X";
const DEFAULT_ROOTS_SYMBOL = "n";
const DEFAULT_OUTERNAMES_SYMBOL = "Y";
var me, spec, nodeDict, edgeDict, portDict, sitesSymbol, innerNamesSymbol, rootsSymbol, outerNamesSymbol, interface, beh = {
postConfigure: function() {
me = this.cnode.parent();
//me.println(me.name());
spec = me.first().text().trim();
nodeDict = {};
edgeDict = {};
portDict = {};
// default values of symbols
sitesSymbol = DEFAULT_SITES_SYMBOL;
innerNamesSymbol = DEFAULT_INNERNAMES_SYMBOL;
rootsSymbol = DEFAULT_ROOTS_SYMBOL;
outerNamesSymbol = DEFAULT_OUTERNAMES_SYMBOL;
interface = {};
me.first().remove();
this.parseSpec(spec);
this.cnode.remove();
if (!me.first()) {
//me.remove();
}
},
parseSpec: function(spec) {
const arr = spec.split("\n");
for (var i = 0; i < arr.length; i++) {
const line = arr[i];
const larr = line.split("=");
const larr0 = larr[0].trim();
const larr1 = larr[1].substring(0, larr[1].length - (larr[1].endsWith(",") ? 1 : 0)).trim(); // remove trailing "," if it exists
//me.println("" + (i+1) + " " + larr0 + " = " + larr1);
switch (larr0) {
case "B":
this.parseBigraph(larr1);
break;
case "Σ":
this.parseSignature(larr1);
break;
case "VB":
this.parseVB(larr1);
break;
case "EB":
this.parseEB(larr1);
break;
case "PB":
this.parsePB(larr1);
break;
case "ctrlB":
this.parseCtrlB(larr1);
break;
case "prntB":
this.parsePrntB(larr1);
break;
case "linkB":
this.parseLinkB(larr1);
break;
default:
// m=0,X=∅,n=1,Y={c,co,t}
const line2 = line.substring(0, line.length-1); // remove trailing ","
const fixedLine = this.preParseInterface(line2);
this.parseInterface(fixedLine);
break;
}
}
},
// (VB,EB,PB,ctrlB,prntB,linkB):〈m,X〉→〈n,Y〉
parseBigraph: function(str) {
const strArr = str.split(":");
const strArr2 = strArr[1].substring(1,strArr[1].length-1).split("〉→〈");
const innerInterface = strArr2[0].split(",");
const outerInterface = strArr2[1].split(",");
//me.println(innerInterface + " " + outerInterface);
sitesSymbol = innerInterface[0]; // "m"
innerNamesSymbol = innerInterface[1]; // "X"
rootsSymbol = outerInterface[0]; // "n"
outerNamesSymbol = outerInterface[1]; // "Y"
//me.println(sitesSymbol + " " + innerNamesSymbol + " " + rootsSymbol + " " + outerNamesSymbol);
},
/**
* @param str example: m=0,X=∅,n=1,Y={c,co,t}
* @return example: m=0|X=∅|n=1|Y={c,co,t}
*/
preParseInterface: function(str) {
// generate 5 segments example: m 0,X ∅,n 1,Y {c,co,t}
const segmentArr = str.split("=");
const seg1 = segmentArr[1].trim();
const seg2 = segmentArr[2].trim();
const seg3 = segmentArr[3].trim();
const seg1len = seg1.length;
const seg2len = seg2.length;
const seg3len = seg3.length;
// fix segments 1 2 3
const segment0 = segmentArr[0].trim();
const segment1 = seg1.substring(0,seg1len-2) + "|" + seg1.substring(seg1len-1);
const segment2 = seg2.substring(0,seg2len-2) + "|" + seg2.substring(seg2len-1);
const segment3 = seg3.substring(0,seg3len-2) + "|" + seg3.substring(seg3len-1);
const segment4 = segmentArr[4].trim();
return segment0 + "=" + segment1 + "=" + segment2 + "=" + segment3 + "=" + segment4;
},
// m=0,X=∅,n=1,Y={c,co,t}
parseInterface: function(str) {
const strArr = str.split("|");
for (var i = 0; i < strArr.length; i++) {
let itemArr = strArr[i].split("=");
switch (itemArr[0]) {
case sitesSymbol: interface[sitesSymbol] = itemArr[1]; break;
case innerNamesSymbol:
// this might be ∅ or the first part of {a,b,c}
interface[innerNamesSymbol] = itemArr[1];
break;
case rootsSymbol: interface[rootsSymbol] = itemArr[1]; break;
case outerNamesSymbol:
// this might be ∅ or the first part of {a,b,c}
interface[outerNamesSymbol] = itemArr[1];
break;
default: me.println("unknown " + strArr[i]); break;
}
}
//me.println(JSON.stringify(interface));
},
// ({get,send,sum},{(get,1),(send,1),(sum,0)})
parseSignature: function(str) {
const str2 = str.substring(2,str.length-2);
const strArr = str2.split("},{");
const ctrlSet = strArr[0].trim();
const portAritySet = strArr[1].trim();
const ctrlSetArr = ctrlSet.split(",");
const portAritySetArr = portAritySet.substring(1,portAritySet.length-1 ).split("),(");
// add nodes to Inheritance Hierarchy
const xhcRoot = $wnd.xh.root().xhc().parent();
let xhcStr = "<_-.ih>";
for (var i = 0; i < ctrlSetArr.length; i++) {
xhcStr += "<" + ctrlSetArr[i] + "/>";
}
xhcStr += "</_-.ih>";
xhcRoot.append(xhcStr);
// add ports to Inheritance Hierarchy class details
let xhcCdStr = "<xholonClassDetails>";
for (var j = 0; j < portAritySetArr.length; j++) {
let portArityPair = portAritySetArr[j].split(",");
// ignore if arity is 0
let xhcName = portArityPair[0];
let portCount = portArityPair[1];
if (portCount > 0) {
xhcCdStr += "<" + xhcName + ' xhType="XhtypePureActiveObject">';
for (var k = 0; k < portCount; k++) {
xhcCdStr += '<port name="port" index="' + k + '" connector="null"></port>';
}
xhcCdStr += "</" + xhcName + ">";
}
}
xhcCdStr += "</xholonClassDetails>";
xhcRoot.append(xhcCdStr);
},
// {a,b,d,e,f,g,h,i,j,k,l}
parseVB: function(str) {
if (str == "∅") {
return; // the set of vertices = the empty set
}
const str2 = str.substring(1,str.length-1);
const strArr = str2.split(",");
for (var i = 0; i < strArr.length; i++) {
let node = strArr[i]; // ex: "a"
nodeDict[node] = null;
}
},
// {q,r,s}
parseEB: function(str) {
if (str == "∅") {
return; // the set of edges = the empty set
}
const str2 = str.substring(1,str.length-1);
const strArr = str2.split(",");
for (var i = 0; i < strArr.length; i++) {
let edge = strArr[i]; // ex: "q"
edgeDict[edge] = null;
}
},
// {p(b,1),p(e,1),p(g,1),p(i,1),p(j,1),p(l,1)}
parsePB: function(str) {
if (str == "∅") {
return; // the set of ports = the empty set
}
const str2 = str.substring(3,str.length-2);
const strArr = str2.split("),p(");
for (var i = 0; i < strArr.length; i++) {
let port = strArr[i]; // ex: "b,1"
portDict[port] = null;
}
},
// {(a,sum),(b,send),(d,sum),(e,get),(f,sum),(g,get),(h,sum),(i,send),(j,get),(k,sum),(l,send)}
parseCtrlB: function(str) {
const str2 = str.substring(2,str.length-2);
const strArr = str2.split("),(");
const root = me; //me.parent();
for (var i = 0; i < strArr.length; i++) {
let pairArr = strArr[i].split(",");
let node = pairArr[0]; // ex: "a"
if (nodeDict[node] == null) {
let ctrl = pairArr[1]; // ex: "sum"
let xhStr = '<' + ctrl + ' roleName="' + node + '"/>';
root.append(xhStr);
nodeDict[node] = root.last();
}
else {
// it might be undefined (it waas not an element in VB), or it might have a non-null value (it may be a duplicate on ctrlB)
me.println("WARNING: control " + node + " is " + nodeDict[node]);
}
}
},
// {(a,0),(f,0),(b,a),(d,b),(e,d),(g,f),(h,g),(i,h),(j,f),(k,j),(l,k)}
parsePrntB: function(str) {
const str2 = str.substring(2,str.length-2);
const strArr = str2.split("),(");
const root = me; //me.parent();
for (var i = 0; i < strArr.length; i++) {
let pairArr = strArr[i].split(",");
let nodeStr = pairArr[0]; // ex: "b"
let prntStr = pairArr[1]; // ex: "a"
let node = nodeDict[nodeStr];
let prnt = root;
if (prntStr != "0") {
prnt = nodeDict[prntStr];
}
if (node == null) {me.println("WARNING: " + nodeStr + " is null");}
else if (prnt == null) {me.println("WARNING: " + nodeStr + " is null");}
else {
prnt.append(node.remove())
}
}
},
// {(p(b,1),c),(p(e,1),co),(p(g,1),c),(p(i,1),co),(p(j,1),c),(p(l,1),t)}
parseLinkB: function(str) {
const str2 = str.substring(2,str.length-2);
const strArr = str2.split("),(");
for (var i = 0; i < strArr.length; i++) {
let pairArr = strArr[i].split(",");
let portStr = pairArr[0] + "," + pairArr[1]; // ex: "p(b,1)"
let portRefStr = pairArr[2]; // ex: "c"
//me.println(portStr + " -> " + portRefStr);
const sourceArr = portStr.substring(2, portStr.length-1).split(","); // ex: "b,1"
const sourceStr = sourceArr[0]; // ex: "b"
const sourcePortNum = sourceArr[1] - 1; // ex: "1"
//me.println(sourceStr + "." + sourcePortNum + " -> " + portRefStr);
// check if this port is defined in portDict
if (portDict[sourceStr + "," + sourcePortNum] == null) {
const srcNode = nodeDict[sourceStr];
const trgNode = nodeDict[portRefStr];
if (srcNode == null) {me.println("WARNING: " + sourceStr + " is null");}
else if (trgNode == null) {me.println("WARNING: " + portRefStr + " is null");}
else {
//me.println(srcNode.name() + "(" + sourcePortNum + ") -> " + trgNode.name());
srcNode.port(sourcePortNum, trgNode);
portDict[sourceStr + "," + sourcePortNum] == trgNode;
}
}
else {
me.println("WARNING: port " + sourceStr + "," + sourcePortNum + " is " + portDict[sourceStr + "," + sourcePortNum]);
}
}
}
}
//# sourceURL=Bigraphbehavior.js
]]></Bigraphbehavior>
<SvgClient><Attribute_String roleName="svgUri"><![CDATA[data:image/svg+xml,
<svg width="100" height="50" xmlns="http://www.w3.org/2000/svg">
<g>
<title>BigraphSystem</title>
<rect id="BigraphSystem" fill="#98FB98" height="50" width="50" x="25" y="0"/>
<g>
<title>BigraphSystem sum</title>
<rect id="BigraphSystem/*" fill="#6AB06A" height="50" width="10" x="80" y="0"/>
</g>
</g>
</svg>
<svg width="618pt" height="417pt"
viewBox="0.00 0.00 618.00 416.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g id="BigraphSystem" class="graph" transform="scale(1 1) rotate(0) translate(4 412.8)">
<title>45</title>
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