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function
findbi
(
e
,
key
,
start
,
end
)
{
while
(
start
<=
end
)
{
var
p
=
Math
.
floor
(
(
start
+
end
)
/
2
)
;
if
(
e
.
links
[
p
]
.
source
<
key
)
{
start
=
p
+
1
;
}
else
{
if
(
e
.
links
[
p
]
.
source
>
key
)
{
end
=
p
-
1
;
}
else
{
return
p
;
}
}
}
return
-
1
;
}
function
findnei
(
a
,
key
,
av
)
{
var
nei
=
[
]
;
if
(
key
[
1
]
)
//virtual node
{
if
(
a
[
a
[
2
]
]
[
a
[
0
]
]
>
0
)
{
//virtual node next
a
[
a
[
2
]
]
[
a
[
0
]
]
-=
av
;
a
[
a
[
0
]
]
[
a
[
2
]
]
-=
av
;
nei
.
push
(
key
)
;
}
else
{
nei
.
push
(
[
a
[
0
]
,
false
,
a
[
2
]
]
)
;
}
}
else
{
for
(
var
i
=
0
;
i
<
a
[
0
]
.
length
;
i
++
)
{
if
(
a
[
key
[
0
]
]
[
i
]
>
0
)
{
if
(
a
[
key
[
0
]
]
[
i
]
>
av
)
nei
.
push
(
[
i
,
true
,
key
[
0
]
]
)
;
// virtual node
else
nei
.
push
(
[
i
,
false
,
key
[
0
]
]
)
;
a
[
key
[
0
]
]
[
i
]
-=
av
;
a
[
i
]
[
key
[
0
]
]
-=
av
;
}
}
}
return
nei
;
}
function
init
(
m
,
n
)
{
var
ar
=
[
]
;
for
(
var
i
=
0
;
i
<
m
;
i
++
)
{
var
art
=
[
]
;
for
(
var
j
=
0
;
j
<
n
;
j
++
)
{
art
.
push
(
0
)
;
}
ar
.
push
(
art
)
;
}
return
ar
;
}
function
init_empty
(
m
)
{
var
ar
=
[
]
;
for
(
var
i
=
0
;
i
<
m
;
i
++
)
{
var
art
=
[
]
;
ar
.
push
(
art
)
;
}
return
ar
;
}
function
a_array
(
ee
)
{
var
a
=
init
(
ee
.
nodes
.
length
,
ee
.
nodes
.
length
)
;
ee
.
links
.
forEach
(
function
(
e
)
{
var
ii
=
0
;
var
jj
=
0
;
ee
.
nodes
.
forEach
(
function
(
n
,
i
)
{
if
(
e
.
source
==
n
.
id
)
ii
=
i
;
else
if
(
e
.
target
==
n
.
id
)
jj
=
i
;
}
)
;
a
[
ii
]
[
jj
]
=
e
.
value
;
a
[
jj
]
[
ii
]
=
e
.
value
;
}
)
;
return
a
;
}
function
a_array_av
(
ee
)
{
var
a
=
init_empty
(
ee
.
nodes
.
length
)
;
var
sum
=
0
;
var
m
=
ee
.
links
.
length
;
ee
.
links
.
forEach
(
function
(
e
)
{
var
ii
=
0
;
var
jj
=
0
;
ee
.
nodes
.
filter
(
function
(
n
,
i
)
{
if
(
e
.
source
==
n
.
id
)
ii
=
i
;
else
if
(
e
.
target
==
n
.
id
)
jj
=
i
;
}
)
;
sum
=
sum
+
(
e
.
value
)
;
a
[
ii
]
.
push
(
{
nei
:
jj
,
val
:
e
.
value
}
)
;
a
[
jj
]
.
push
(
{
nei
:
ii
,
val
:
e
.
value
}
)
;
}
)
;
return
[
a
,
sum
/
m
]
;
}
function
calculate_m
(
ee
)
{
var
sum
=
0
;
var
m
=
ee
.
links
.
length
;
ee
.
links
.
forEach
(
function
(
e
)
{
var
ii
=
0
;
var
jj
=
0
;
/*ee.nodes.filter(function(n,i){
if (e.source==n.id)
ii=i;
else
if (e.target==n.id)
jj=i;
});*/
sum
=
sum
+
e
.
value
;
}
)
;
return
sum
;
}
function
a_array_ext
(
arr
,
av
)
{
var
l
=
arr
.
length
;
for
(
var
iii
=
0
;
iii
<
l
;
iii
++
)
{
for
(
var
jjj
=
0
;
jjj
<
arr
[
iii
]
.
length
;
jjj
++
)
{
var
n
=
Math
.
round
(
arr
[
iii
]
[
jjj
]
.
val
/
av
)
;
var
nei
=
arr
[
iii
]
[
jjj
]
.
nei
;
if
(
n
>
1
)
{
arr
[
iii
]
[
jjj
]
=
{
nei
:
arr
.
length
,
val
:
av
,
ori
:
nei
}
;
//arr[iii][jjj].nei = arr.length;
//arr[iii][jjj].val = av;
arr
.
push
(
[
{
nei
:
iii
,
val
:
av
,
ori
:
nei
}
,
{
nei
:
nei
,
val
:
av
,
ori
:
iii
}
]
)
;
for
(
var
z
=
2
;
z
<
n
;
z
++
)
{
var
ll
=
arr
.
length
;
//arr[ll-1][1].nei = ll;
arr
[
ll
-
1
]
[
1
]
=
{
nei
:
ll
,
var
:
av
,
ori
:
iii
}
;
arr
.
push
(
[
{
nei
:
ll
-
1
,
val
:
av
}
,
{
nei
:
nei
,
val
:
av
,
ori
:
nei
}
]
)
;
}
arr
[
nei
]
.
filter
(
function
(
n
,
i
)
{
if
(
n
.
nei
==
iii
)
{
arr
[
nei
]
.
splice
(
i
,
1
,
{
nei
:
arr
.
length
-
1
,
val
:
av
,
ori
:
iii
}
)
;
//n.val = av;
//n.nei = arr.length-1;//last virtual node
}
}
)
;
}
}
}
return
[
arr
,
av
]
;
}
function
finditem
(
grouping
,
li
,
graph
)
{
var
g1
=
-
1
;
var
g2
=
-
1
;
for
(
var
i
=
0
;
(
i
<
grouping
.
length
)
&&
(
g1
==
-
1
||
g2
==
-
1
)
;
i
++
)
{
for
(
var
j
=
0
;
(
j
<
grouping
[
i
]
.
length
)
&&
(
g1
==
-
1
||
g2
==
-
1
)
;
j
++
)
{
if
(
g1
==
-
1
&&
grouping
[
i
]
[
j
]
==
li
[
0
]
)
g1
=
i
;
if
(
g2
==
-
1
&&
grouping
[
i
]
[
j
]
==
li
[
1
]
)
g2
=
i
;
}
}
return
[
g1
,
g2
]
;
}
function
clone
(
obj
)
{
if
(
null
==
obj
||
"object"
!=
typeof
obj
)
return
obj
;
var
copy
=
obj
.
constructor
(
)
;
for
(
var
attr
in
obj
)
{
if
(
obj
.
hasOwnProperty
(
attr
)
)
copy
[
attr
]
=
obj
[
attr
]
;
}
return
copy
;
}
function
copyA
(
a
)
{
var
b
=
[
]
;
a
.
forEach
(
function
(
e
)
{
var
bb
=
[
]
;
e
.
forEach
(
function
(
e
)
{
bb
.
push
(
clone
(
e
)
)
;
}
)
;
b
.
push
(
bb
)
;
}
)
;
return
b
;
}
//virtual nodes
function
between_e
(
graph
)
{
var
alink_o
=
a_array_av
(
graph
)
;
// orgiginal
var
av
=
alink_o
[
1
]
;
alink_o
=
alink_o
[
0
]
;
var
alink_fix
=
a_array_ext
(
alink_o
,
av
)
[
0
]
;
// add virtual nodes
var
num_n
=
graph
.
nodes
.
length
;
// num of node
var
step
=
[
]
;
var
num_l
=
graph
.
links
.
length
;
//document.write("</br> av: "+av);
while
(
step
.
length
!=
graph
.
links
.
length
)
{
//var alink_oc = copyA(alink_o);
//document.write("</br> old array size: "+alink_o[3][0].nei);
//var alink_fix = a_array_ext(alink_oc,av); // add virtual nodes
//document.write("</br> old array size: "+alink_o[3][0].nei);
//var alink = alink_fix[0]; //fixed
// calculate
var
ebs
=
init
(
num_n
,
num_n
)
;
var
max_ebs
=
[
0
,
0
,
0
]
;
var
start_time
=
performance
.
now
(
)
;
for
(
var
s
=
0
;
s
<
num_n
;
s
++
)
{
var
S
=
[
]
;
var
Leaf
=
[
]
;
var
Pathu
=
[
]
;
var
Pathd
=
[
]
;
var
d
=
[
]
;
var
w
=
[
]
;
d
[
s
]
=
0
;
w
[
s
]
=
1
;
var
Q
=
[
]
;
Q
.
push
(
s
)
;
while
(
Q
.
length
!=
0
)
{
var
i
=
Q
.
shift
(
)
;
if
(
i
<
num_n
)
S
.
push
(
i
)
;
var
l
=
Q
.
length
;
//document.write("</br>"+i+": ");
//console.log(" to: "+i);
alink_fix
[
i
]
.
forEach
(
function
(
e
,
indd
)
{
var
j
=
e
.
nei
;
if
(
d
[
j
]
==
null
)
{
d
[
j
]
=
d
[
i
]
+
1
;
w
[
j
]
=
w
[
i
]
;
Q
.
push
(
j
)
;
if
(
i
<
num_n
)
{
//not virtual node
Pathu
[
j
]
=
[
i
]
;
if
(
j
<
num_n
)
{
if
(
Pathd
[
i
]
==
null
)
Pathd
[
i
]
=
[
j
]
;
else
Pathd
[
i
]
.
push
(
j
)
;
}
//console.log(i+" Pathd "+ Pathd[i]);
}
else
{
Pathu
[
j
]
=
Pathu
[
i
]
;
if
(
j
<
num_n
)
{
if
(
Pathd
[
alink_fix
[
i
]
[
indd
]
.
ori
]
==
null
)
Pathd
[
alink_fix
[
i
]
[
indd
]
.
ori
]
=
[
j
]
;
else
Pathd
[
alink_fix
[
i
]
[
indd
]
.
ori
]
.
push
(
j
)
;
}
//console.log(alink_fix[i][indd].ori+" Pathd "+ Pathd[alink_fix[i][indd].ori]);
}
//console.log(j+" Pathu "+ Pathu[j]);
}
else
{
if
(
d
[
j
]
==
d
[
i
]
+
1
)
{
w
[
j
]
=
w
[
j
]
+
w
[
i
]
;
if
(
i
<
num_n
)
{
//not virtual node
Pathu
[
j
]
.
push
(
i
)
;
if
(
j
<
num_n
)
{
if
(
Pathd
[
i
]
==
null
)
Pathd
[
i
]
=
[
j
]
;
else
Pathd
[
i
]
.
push
(
j
)
;
}
//if j is virtual , j won't be visit second time
}
else
{
if
(
j
<
num_n
)
{
Pathu
[
j
]
.
concat
(
Pathu
[
i
]
)
;
if
(
Pathd
[
alink_fix
[
i
]
[
indd
]
.
ori
]
==
null
)
Pathd
[
alink_fix
[
i
]
[
indd
]
.
ori
]
=
[
j
]
;
else
Pathd
[
alink_fix
[
i
]
[
indd
]
.
ori
]
.
concat
(
Pathd
[
j
]
)
;
}
}
//console.log(i+" Pathd "+ Pathd[i]);
//console.log(j+" Pathu "+ Pathu[j]);
}
}
//document.write("</br>"+" - "+e.nei+": "+"d :"+d[e.nei]+"w :"+w[e.nei]);
}
)
;
if
(
Q
.
length
==
l
&&
(
i
!=
s
)
&&
(
i
<
num_n
)
)
Leaf
.
push
(
i
)
;
}
/*for (var i=0;i<num_n;i++){
document.write("</br>"+" - "+i+" - w:"+w[i]);
document.write("</br>"+" --- u");
if(Pathu[i]!=null)
Pathu[i].forEach(function(e){document.write("- "+e);});
document.write("</br>"+" --- d");
if(Pathd[i]!=null)
Pathd[i].forEach(function(e){document.write("- "+e);});
};*/
var
eb
=
init
(
num_n
,
num_n
)
;
var
gene
=
[
]
;
//Leaf
/*while(Leaf.length!=0){
var t=Leaf.pop();
console.log("list Leaf: "+t);
//S.filter(function(e,inde){if (e==t){ S.splice(inde,1); return;}});
//document.write("</br>"+" -Leaf "+t);
while (Pathu[t].length!=0){
var i = Pathu[t].pop();
eb[i][t] += w[i]/w[t];
eb[t][i] += w[i]/w[t];
ebs[i][t] += w[i]/w[t];
ebs[t][i] += w[i]/w[t];
//console.log(ebs[i][t]);
if (ebs[i][t]>max_ebs[0]){
max_ebs[0]=ebs[i][t];
max_ebs[1]=i;
max_ebs[2]=t;
}
if (ebs[t][i]>max_ebs[0]){
max_ebs[0]=ebs[t][i];
max_ebs[1]=t;
max_ebs[2]=i;
}
}
}*/
//document.write("</br>"+" ----- ");
//document.write("</br>"+S);
//cont
S
.
splice
(
0
,
1
)
;
while
(
S
.
length
!=
0
)
{
var
j
=
S
.
pop
(
)
;
//console.log(j+" -- "+d[j]);
if
(
Pathd
[
j
]
!=
null
)
{
//document.write("</br> -- "+j);
var
sumb
=
1
;
while
(
Pathd
[
j
]
.
length
!=
0
)
{
var
jj
=
Pathd
[
j
]
.
pop
(
)
;
sumb
+=
eb
[
j
]
[
jj
]
;
}
if
(
Pathu
[
j
]
!=
null
)
{
while
(
Pathu
[
j
]
.
length
!=
0
)
{
var
i
=
Pathu
[
j
]
.
pop
(
)
;
eb
[
i
]
[
j
]
=
w
[
i
]
/
w
[
j
]
*
sumb
;
//eb[j][i]+=w[i]/w[j]*sumb;
ebs
[
i
]
[
j
]
+=
w
[
i
]
/
w
[
j
]
*
sumb
;
//ebs[j][i]+=w[i]/w[j]*sumb;
//console.log("2-10: "+ebs[2][10]+" 10-12: "+ebs[10][12]+"10-9: "+ebs[9][10]);
//console.log(ebs[i][t]);
if
(
ebs
[
i
]
[
j
]
>
max_ebs
[
0
]
)
{
max_ebs
[
0
]
=
ebs
[
i
]
[
j
]
;
max_ebs
[
1
]
=
i
;
max_ebs
[
2
]
=
j
;
//console.log("i: "+max_ebs[1]+" j: "+max_ebs[2]+" max "+max_ebs[0]);
//document.write("</br>"+"max "+ max_ebs);
}
else
{
if
(
ebs
[
i
]
[
j
]
==
max_ebs
[
0
]
)
{
if
(
Math
.
abs
(
d
[
i
]
-
d
[
j
]
)
<
Math
.
abs
(
d
[
max_ebs
[
1
]
]
-
d
[
max_ebs
[
2
]
]
)
)
{
max_ebs
[
0
]
=
ebs
[
i
]
[
j
]
;
max_ebs
[
1
]
=
i
;
max_ebs
[
2
]
=
j
;
//console.log("i: "+max_ebs[1]+" j: "+max_ebs[2]+" max "+max_ebs[0]);
//document.write("</br>"+"max "+ max_ebs);
}
}
}
}
}
}
else
{
while
(
Pathu
[
j
]
.
length
!=
0
)
{
var
i
=
Pathu
[
j
]
.
pop
(
)
;
eb
[
i
]
[
j
]
=
w
[
i
]
/
w
[
j
]
;
//eb[j][i] += w[i]/w[j];
ebs
[
i
]
[
j
]
+=
w
[
i
]
/
w
[
j
]
;
// ebs[j][i] += w[i]/w[j];
if
(
ebs
[
i
]
[
j
]
>
max_ebs
[
0
]
)
{
max_ebs
[
0
]
=
ebs
[
i
]
[
j
]
;
max_ebs
[
1
]
=
i
;
max_ebs
[
2
]
=
j
;
//console.log("i: "+max_ebs[1]+" j: "+max_ebs[2]+" max "+max_ebs[0]);
}
else
{
if
(
ebs
[
i
]
[
j
]
==
max_ebs
[
0
]
)
{
if
(
Math
.
abs
(
d
[
i
]
-
d
[
j
]
)
<
Math
.
abs
(
d
[
max_ebs
[
1
]
]
-
d
[
max_ebs
[
2
]
]
)
)
{
max_ebs
[
0
]
=
ebs
[
i
]
[
j
]
;
max_ebs
[
1
]
=
i
;
max_ebs
[
2
]
=
j
;
//console.log("i: "+max_ebs[1]+" j: "+max_ebs[2]+" max "+max_ebs[0]);
//document.write("</br>"+"max "+ max_ebs);
}
}
}
}
}
}
//console.log("----end---- "+s);
}
var
end_time_b
=
performance
.
now
(
)
;
//console.log("Time for old technique");
//console.log(end_time_b-start_time);
if
(
max_ebs
[
0
]
!=
0
)
{
step
.
push
(
[
max_ebs
[
1
]
,
max_ebs
[
2
]
]
)
;
//av = av*num_l;
//document.write("</br>"+"max "+ max_ebs[0]);
for
(
var
i
=
0
;
i
<
alink_fix
[
max_ebs
[
1
]
]
.
length
;
i
++
)
{
//document.write("</br>"+"-- "+ alink_o[max_ebs[1]][i].nei);
if
(
alink_fix
[
max_ebs
[
1
]
]
[
i
]
.
nei
==
max_ebs
[
2
]
||
alink_fix
[
max_ebs
[
1
]
]
[
i
]
.
ori
==
max_ebs
[
2
]
)
{
//av = av - alink_o[max_ebs[1]][i].val;
//num_l--;
//av = av/num_l;
alink_fix
[
max_ebs
[
1
]
]
.
splice
(
i
,
1
)
;
break
;
}
}
for
(
var
i
=
0
;
i
<
alink_fix
[
max_ebs
[
2
]
]
.
length
;
i
++
)
{
//document.write("</br>"+"--- "+ alink_o[max_ebs[2]][i].nei);
if
(
alink_fix
[
max_ebs
[
2
]
]
[
i
]
.
nei
==
max_ebs
[
1
]
||
alink_fix
[
max_ebs
[
2
]
]
[
i
]
.
ori
==
max_ebs
[
1
]
)
{
alink_fix
[
max_ebs
[
2
]
]
.
splice
(
i
,
1
)
;
break
;
}
}
}
//console.log("----step: "+ step+" av"+av+"</br>");
}
return
step
;
}
function
Q_init
(
A
,
m
,
a_e
)
{
var
n
=
A
.
length
;
var
Q
=
0
;
for
(
var
i
=
0
;
i
<
n
;
i
++
)
{
var
sum
=
0
;
for
(
var
j
=
0
;
j
<
n
;
j
++
)
{
sum
+=
A
[
i
]
[
j
]
;
}
a_e
.
push
(
sum
/
2
/
m
)
;
Q
-=
Math
.
pow
(
sum
/
2
/
m
,
2
)
;
}
return
Q
;
}
function
delta_Q
(
i
,
j
,
m
,
A
,
a_e
)
{
var
n
=
A
.
length
;
var
delta_Q
=
2
*
(
A
[
i
]
[
j
]
/
2
/
m
-
a_e
[
i
]
*
a_e
[
j
]
)
;
//update
A
[
i
]
[
i
]
+=
A
[
j
]
[
j
]
+
A
[
i
]
[
j
]
+
A
[
j
]
[
i
]
;
A
[
j
]
[
j
]
=
0
;
A
[
j
]
[
i
]
=
0
;
A
[
i
]
[
j
]
=
0
;
var
sum
=
0
;
for
(
var
k
=
0
;
k
<
n
;
k
++
)
{
if
(
k
!=
i
&&
k
!=
j
)
{
A
[
i
]
[
k
]
=
A
[
i
]
[
k
]
+
A
[
j
]
[
k
]
;
A
[
k
]
[
i
]
=
A
[
i
]
[
k
]
;
A
[
j
]
[
k
]
=
0
;
A
[
k
]
[
j
]
=
0
;
}
sum
+=
A
[
i
]
[
k
]
;
}
a_e
[
i
]
=
sum
/
2
/
m
;
a_e
[
j
]
=
0
;
return
delta_Q
;
}
function
takeaname
(
d
)
{
return
d
.
label
!=
null
?
d
.
label
:
(
d
.
name
!=
null
?
d
.
name
:
d
.
id
)
;
}
function
tree_mapingv3
(
step
,
graph
)
{
var
grouping
=
[
]
;
var
ed
=
step
.
pop
(
)
;
var
lv
=
1
;
var
m
=
calculate_m
(
graph
)
;
var
A
=
a_array
(
graph
)
;
var
a_e
=
[
]
;
var
Q
=
[
]
;
var
Q_t
=
Q_init
(
A
,
m
,
a_e
)
;
Q
.
push
(
Q_t
)
;
grouping
.
push
(
ed
)
;
// join 2 nodes together
Q_t
+=
delta_Q
(
ed
[
0
]
,
ed
[
1
]
,
m
,
A
,
a_e
)
;
//----
Q
.
push
(
Q_t
)
;
var
hi
=
[
{
name
:
ed
,
children
:
[
{
name
:
takeaname
(
graph
.
nodes
[
ed
[
0
]
]
)
,
depth
:
0
}
,
{
name
:
takeaname
(
graph
.
nodes
[
ed
[
1
]
]
)
,
depth
:
0
}
]
,
depth
:
lv
,
Q
:
Q_t
}
]
;
while
(
step
.
length
!=
0
)
{
var
li
=
step
.
pop
(
)
;
// 4 main case
for
(
var
i
=
0
;
i
<
grouping
.
length
;
i
++
)
{
var
g
=
finditem
(
grouping
,
li
,
graph
)
;
}
var
g1
=
g
[
0
]
;
var
g2
=
g
[
1
]
;
if
(
g1
!=
g2
)
{
lv
++
;
if
(
g1
!=
-
1
&&
g2
!=
-
1
)
{
// 2 groups -> new group
//Q
Q_t
+=
delta_Q
(
grouping
[
g1
]
[
0
]
,
grouping
[
g2
]
[
0
]
,
m
,
A
,
a_e
)
;
Q
.
push
(
Q_t
)
;
//move
grouping
.
splice
(
g1
,
1
,
grouping
[
g1
]
.
concat
(
grouping
[
g2
]
)
)
;
grouping
.
splice
(
g2
,
1
)
;
var
hi_t
=
[
]
;
hi_t
.
push
(
hi
[
g1
]
)
;
hi_t
.
push
(
hi
[
g2
]
)
;
hi
[
g1
]
=
{
name
:
li
,
children
:
hi_t
,
depth
:
lv
,
Q
:
Q_t
}
;
hi
.
splice
(
g2
,
1
)
;
//document.write("case 1 "+g1+" "+g2+" "+JSON.stringify(hi)+"</br>");
}
else
{
// 1 element + 1 group -> new group
var
li_t
=
li
;
if
(
g2
==
-
1
)
{
// li[1] is new element
li_t
[
0
]
=
li_t
[
1
]
;
}
else
{
g1
=
g2
;
}
//Q
Q_t
+=
delta_Q
(
grouping
[
g1
]
[
0
]
,
li
[
0
]
,
m
,
A
,
a_e
)
;
Q
.
push
(
Q_t
)
;
//move
grouping
[
g1
]
.
push
(
li
[
0
]
)
;
hi
[
g1
]
=
{
name
:
li
,
children
:
[
hi
[
g1
]
]
,
depth
:
lv
,
Q
:
Q_t
}
;
hi
[
g1
]
.
children
.
push
(
{
name
:
takeaname
(
graph
.
nodes
[
li_t
[
0
]
]
)
,
depth
:
0
}
)
;
//document.write("case 2 "+JSON.stringify(hi)+"</br>");
}
}
else
{
if
(
g1
==
-
1
)
{
lv
++
;
//Q
Q_t
+=
delta_Q
(
li
[
0
]
,
li
[
1
]
,
m
,
A
,
a_e
)
;
Q
.
push
(
Q_t
)
;
//move
grouping
.
push
(
li
)
;
hi
.
push
(
{
name
:
li
,
children
:
[
{
name
:
takeaname
(
graph
.
nodes
[
li
[
0
]
]
)
,
depth
:
0
}
,
{
name
:
takeaname
(
graph
.
nodes
[
li
[
1
]
]
)
,
depth
:
0
}
]
,
depth
:
lv
,
Q
:
Q_t
}
)
;
//document.write("case 3 "+JSON.stringify(hi)+"</br>");
}
}
}
if
(
hi
.
length
==
1
)
{
return
[
hi
[
0
]
,
Q
]
;
}
else
{
hi
[
0
]
=
{
name
:
"join all"
,
children
:
[
hi
[
0
]
]
,
depth
:
lv
+
1
,
Q
:
Q_t
}
;
while
(
grouping
.
length
!=
1
)
{
Q_t
+=
delta_Q
(
grouping
[
0
]
[
0
]
,
grouping
[
1
]
[
0
]
,
m
,
A
,
a_e
)
;
grouping
.
splice
(
0
,
1
,
grouping
[
0
]
.
concat
(
grouping
[
1
]
)
)
;
grouping
.
splice
(
1
,
1
)
;
hi
[
0
]
.
children
.
push
(
hi
[
1
]
)
;
hi
.
splice
(
1
,
1
)
;
}
Q
.
push
(
Q_t
)
;
return
[
hi
[
0
]
,
Q
]
;
}
}
//Start Vinh's code
function
make2dArray
(
len
)
{
var
a
=
[
]
;
while
(
a
.
push
(
[
]
)
<
len
)
;
return
a
;
}
function
graph_nodes_random
(
nodes
,
size
)
{
var
oldnodes
=
[
]
;
for
(
i
=
0
;
i
<
nodes
;
i
++
)
{
oldnodes
.
push
(
i
)
}
var
newnodes
=
[
]
;
for
(
i
=
0
;
i
<
size
;
i
++
)
{
var
value
=
oldnodes
[
Math
.
floor
(
oldnodes
.
length
*
Math
.
random
(
)
)
]
;
var
index
=
oldnodes
.
indexOf
(
value
)
;
newnodes
.
push
(
value
)
;
oldnodes
.
splice
(
index
,
1
)
;
}
return
newnodes
.
sort
(
function
(
a
,
b
)
{
return
a
-
b
;
}
)
;
}
function
edge_betweenness_centrality
(
graph
,
k
=
'none'
,
normalized
=
true
,
weight
)
{
var
num_node
=
graph
.
nodes
.
length
;
var
num_link
=
graph
.
links
.
length
;
//var tempgraph = Object.assign({}, graph.nodes);
var
betweenness
=
new
Object
(
)
;
for
(
var
linkitem
=
0
;
linkitem
<
graph
.
links
.
length
;
linkitem
++
)
{
for
(
var
nodeItem
=
0
;
nodeItem
<
num_node
;
nodeItem
++
)
{
if
(
graph
.
nodes
[
nodeItem
]
.
id
==
graph
.
links
[
linkitem
]
.
source
)
{
graph
.
links
[
linkitem
]
.
source
=
nodeItem
;
}
if
(
graph
.
nodes
[
nodeItem
]
.
id
==
graph
.
links
[
linkitem
]
.
target
)
{
graph
.
links
[
linkitem
]
.
target
=
nodeItem
;
}
}
}
var
step
=
[
]
;
var
nodes
;
var
neighbours
=
make2dArray
(
num_node
)
;
for
(
var
i
=
0
;
i
<
graph
.
links
.
length
;
i
++
)
{
var
source
=
graph
.
links
[
i
]
.
source
;
var
target
=
graph
.
links
[
i
]
.
target
;
var
value
=
graph
.
links
[
i
]
.
value
;
neighbours
[
source
]
.
push
(
[
target
,
value
]
)
;
neighbours
[
target
]
.
push
(
[
source
,
value
]
)
;
}
if
(
k
!==
'none'
)
{
nodes
=
graph_nodes_random
(
num_node
,
k
)
}
else
{
nodes
=
graph_nodes_random
(
num_node
,
num_node
)
;
}
var
start_time
=
performance
.
now
(
)
;
while
(
step
.
length
!=
graph
.
links
.
length
)
{
for
(
i
=
0
;
i
<
num_node
;
i
++
)
{
betweenness
[
i
]
=
0.0
}
for
(
var
i
=
0
;
i
<
graph
.
links
.
length
;
i
++
)
{
var
source
=
graph
.
links
[
i
]
.
source
;
var
target
=
graph
.
links
[
i
]
.
target
;
betweenness
[
source
+
","
+
target
]
=
0.0
;
}
var
start_time
=
performance
.
now
(
)
;
for
(
s
=
0
;
s
<
nodes
.
length
;
s
++
)
{
if
(
weight
==
true
)
{
var
SPSigma
=
_single_source_dijkstra_path_basic
(
neighbours
,
nodes
[
s
]
,
weight
)
;
var
S
=
SPSigma
[
0
]
;
var
P
=
SPSigma
[
1
]
;
var
sigma
=
SPSigma
[
2
]
;
betweenness
=
_accumulate_edges
(
betweenness
,
S
,
P
,
sigma
,
nodes
[
s
]
)
;
}
else
{
var
SPSigma
=
_single_source_shortest_path_basic
(
neighbours
,
nodes
[
s
]
)
;
var
S
=
SPSigma
[
0
]
;
var
P
=
SPSigma
[
1
]
;
var
sigma
=
SPSigma
[
2
]
;
betweenness
=
_accumulate_edges
(
betweenness
,
S
,
P
,
sigma
,
nodes
[
s
]
)
;
}
}
for
(
n
=
0
;
n
<
num_node
;
n
++
)
{
delete
betweenness
[
n
]
;
}
var
scale
=
1.0
/
(
(
num_node
)
*
(
num_node
-
1
)
)
for
(
var
key
in
betweenness
)
{
if
(
!
betweenness
.
hasOwnProperty
(
key
)
)
continue
;
betweenness
[
key
]
*=
scale
;
}
var
obkey
,
obvalue
=
0
;
for
(
var
key
in
betweenness
)
{
if
(
betweenness
[
key
]
>
obvalue
)
{
obvalue
=
betweenness
[
key
]
;
obkey
=
key
.
split
(
","
)
.
map
(
Number
)
;
}
}
step
.
push
(
[
obkey
[
0
]
,
obkey
[
1
]
]
)
;
for
(
i
=
0
;
i
<
neighbours
[
obkey
[
0
]
]
.
length
;
i
++
)
{
if
(
neighbours
[
obkey
[
0
]
]
[
i
]
[
0
]
===
obkey
[
1
]
)
{
neighbours
[
obkey
[
0
]
]
.
splice
(
i
,
1
)
;
}
}
for
(
i
=
0
;
i
<
neighbours
[
obkey
[
1
]
]
.
length
;
i
++
)
{
if
(
neighbours
[
obkey
[
1
]
]
[
i
]
[
0
]
===
obkey
[
0
]
)
{
neighbours
[
obkey
[
1
]
]
.
splice
(
i
,
1
)
;
}
}
}
var
end_time_b
=
performance
.
now
(
)
;
console
.
log
(
"Time to run betweenness brandes"
)
;
console
.
log
(
end_time_b
-
start_time
)
;
return
step
;
}
function
_single_source_dijkstra_path_basic
(
G
,
s
,
weight
=
'weight'
)
{
var
S
=
[
]
,
P
=
new
Object
(
)
,
sigma
=
new
Object
(
)
,
D
=
new
Object
(
)
;
var
Q
=
[
]
;
for
(
var
v
=
0
;
v
<
G
.
length
;
v
++
)
{
P
[
v
]
=
[
]
;
sigma
[
v
]
=
0
;
}
sigma
[
s
]
=
1.0
seen
=
new
Object
(
)
;
seen
[
s
]
=
0
;
var
count
=
0
;
Q
.
push
(
[
0
,
count
,
s
,
s
]
)
;
while
(
Q
.
length
>
0
)
{
Q
.
sort
(
function
(
a
,
b
)
{
return
a
[
0
]
-
b
[
0
]
;
}
)
var
getvalue
=
Q
.
shift
(
)
;
var
dist
=
getvalue
[
0
]
;
var
_
=
getvalue
[
1
]
;
var
pred
=
getvalue
[
2
]
;
var
v
=
getvalue
[
3
]
;
if
(
D
.
hasOwnProperty
(
v
)
)
{
continue
;
}
sigma
[
v
]
+=
sigma
[
pred
]
;
S
.
push
(
v
)
;
D
[
v
]
=
dist
;
for
(
var
link
=
0
;
link
<
G
[
v
]
.
length
;
link
++
)
{
var
vw_dist
=
dist
+
G
[
v
]
[
link
]
[
1
]
;
var
w
=
G
[
v
]
[
link
]
[
0
]
;
if
(
!
D
.
hasOwnProperty
(
w
)
&&
(
!
seen
.
hasOwnProperty
(
w
)
||
vw_dist
<
seen
[
w
]
)
)
{
seen
[
w
]
=
vw_dist
;
Q
.
push
(
[
vw_dist
,
++
count
,
v
,
w
]
)
;
sigma
[
w
]
=
0.0
;
P
[
w
]
=
[
v
]
;
}
else
if
(
vw_dist
===
seen
[
w
]
)
{
sigma
[
w
]
+=
sigma
[
v
]
;
P
[
w
]
.
push
(
v
)
}
}
}
return
[
S
,
P
,
sigma
]
;
}
function
_single_source_shortest_path_basic
(
G
,
s
)
{
var
S
=
[
]
,
P
=
new
Object
(
)
,
sigma
=
new
Object
(
)
,
D
=
new
Object
(
)
;
for
(
var
item
=
0
;
item
<
G
.
length
;
item
++
)
{
P
[
item
]
=
[
]
;
sigma
[
item
]
=
0
;
}
sigma
[
s
]
=
1
;
D
[
s
]
=
0
;
var
Q
=
[
]
;
Q
.
push
(
s
)
;
while
(
Q
.
length
>
0
)
{
v
=
Q
.
shift
(
)
;
S
.
push
(
v
)
;
Dv
=
D
[
v
]
;
sigmav
=
sigma
[
v
]
;
for
(
var
item
=
0
;
item
<
G
[
v
]
.
length
;
item
++
)
{
if
(
!
D
.
hasOwnProperty
(
G
[
v
]
[
item
]
[
0
]
)
)
{
Q
.
push
(
G
[
v
]
[
item
]
[
0
]
)
;
D
[
G
[
v
]
[
item
]
[
0
]
]
=
Dv
+
1
;
}
if
(
D
[
G
[
v
]
[
item
]
[
0
]
]
===
Dv
+
1
)
{
sigma
[
G
[
v
]
[
item
]
[
0
]
]
+=
sigmav
;
P
[
G
[
v
]
[
item
]
[
0
]
]
.
push
(
v
)
;
}
}
}
return
[
S
,
P
,
sigma
]
;
}
function
_accumulate_edges
(
betweenness
,
S
,
P
,
sigma
,
s
)
{
var
delta
=
new
Object
(
)
;
for
(
var
i
=
0
;
i
<
S
.
length
;
i
++
)
{
delta
[
S
[
i
]
]
=
0
;
}
while
(
S
.
length
>
0
)
{
var
w
=
S
.
pop
(
)
;
var
coeff
=
(
1.0
+
delta
[
w
]
)
/
sigma
[
w
]
;
for
(
var
v
=
0
;
v
<
P
[
w
]
.
length
;
v
++
)
{
var
c
=
sigma
[
P
[
w
]
[
v
]
]
*
coeff
;
var
p1
=
P
[
w
]
[
v
]
+
","
+
w
;
var
p2
=
w
+
","
+
P
[
w
]
[
v
]
;
if
(
!
betweenness
.
hasOwnProperty
(
p1
)
)
{
betweenness
[
(
p2
)
]
+=
c
;
}
else
{
betweenness
[
(
p1
)
]
+=
c
;
}
delta
[
P
[
w
]
[
v
]
]
+=
c
;
}
if
(
w
!==
P
[
w
]
[
v
]
)
{
betweenness
[
w
]
+=
delta
[
w
]
;
}
}
return
betweenness
;
}
function
_getV
(
graph
)
{
var
alink_o
=
a_array_av
(
graph
)
;
// orgiginal
var
av
=
alink_o
[
1
]
;
alink_o
=
alink_o
[
0
]
;
var
alink_fix
=
a_array_ext
(
alink_o
,
av
)
[
0
]
;
var
adjList
=
[
]
;
for
(
i
=
0
;
i
<
alink_fix
.
length
;
i
++
)
{
adjList
[
i
]
=
[
]
;
for
(
j
=
0
;
j
<
alink_fix
[
i
]
.
length
;
j
++
)
{
adjList
[
i
]
.
push
(
alink_fix
[
i
]
[
j
]
.
nei
)
}
}
return
adjList
;
}
function
_removeEdge
(
_graph
,
_edge
)
{
_graph
.
links
.
forEach
(
function
(
d
,
i
)
{
if
(
d
.
source
===
_edge
[
0
]
&&
d
.
target
===
_edge
[
1
]
||
d
.
source
===
_edge
[
1
]
&&
d
.
target
===
_edge
[
0
]
)
{
_graph
.
links
.
splice
(
i
,
1
)
;
}
}
)
;
return
_graph
;
}
function
_betweennness_virtual
(
graph
)
{
var
step
=
[
]
;
var
alink_o
=
a_array_av
(
graph
)
;
// orgiginal
var
av
=
alink_o
[
1
]
;
alink_o
=
alink_o
[
0
]
;
var
totaldegree
=
0
;
for
(
i
=
0
;
i
<
alink_o
.
length
;
i
++
)
{
totaldegree
+=
alink_o
[
i
]
.
length
;
}
var
VirtualAdj
=
a_array_ext
(
alink_o
,
av
)
[
0
]
;
console
.
log
(
"Total virtual nodes:"
+
VirtualAdj
.
length
)
var
betweenness
=
new
Object
(
)
;
var
nodes
=
[
]
;
var
num_node
=
graph
.
nodes
.
length
;
var
templink
=
graph
.
links
.
filter
(
function
(
d
)
{
if
(
d
.
value
>
1
)
return
d
;
}
)
console
.
log
(
templink
)
var
random_node
=
Math
.
floor
(
Math
.
random
(
)
*
graph
.
nodes
.
length
)
var
pred
=
prececessorV_length
(
VirtualAdj
,
random_node
,
graph
.
nodes
.
length
)
;
var
arrayvalue
=
Object
.
values
(
pred
)
.
sort
(
function
(
a
,
b
)
{
return
b
-
a
;
}
)
;
var
VDG
=
arrayvalue
[
0
]
+
arrayvalue
[
1
]
;
var
sigma
=
0.1
,
delta
=
0.1
,
c
=
0.5
;
var
d
=
Math
.
floor
(
Math
.
log2
(
VDG
)
-
2
)
+
1
+
Math
.
log
(
1
/
delta
)
;
var
r
=
c
/
Math
.
pow
(
sigma
,
2
)
*
d
;
for
(
var
i
=
0
;
i
<
graph
.
nodes
.
length
;
i
++
)
{
nodes
.
push
(
i
)
;
}
console
.
log
(
"2-approx Diameter"
)
console
.
log
(
VDG
)
console
.
log
(
"Number of real nodes: "
+
graph
.
nodes
.
length
)
;
console
.
log
(
"Number of virtual nodes: "
+
VirtualAdj
.
length
)
;
console
.
log
(
"Number of iteration on sampling: "
+
r
)
graph
.
links
.
forEach
(
function
(
d
)
{
betweenness
[
d
.
source
+
','
+
d
.
target
]
=
0
;
}
)
;
// var start_time = performance.now();
// while (step.length != graph.links.length) {
var
start_time
=
performance
.
now
(
)
;
while
(
step
.
length
!=
graph
.
links
.
length
)
{
for
(
i
=
0
;
i
<
r
;
i
++
)
{
var
s
=
Math
.
floor
(
Math
.
random
(
)
*
nodes
.
length
)
// var s= i;
var
SPSigma
=
_single_source_shortest_path_basic_virtual_nodes
(
VirtualAdj
,
s
,
nodes
)
;
var
S
=
SPSigma
[
0
]
;
var
P
=
SPSigma
[
1
]
;
var
sigma
=
SPSigma
[
2
]
;
betweenness
=
_accumulate_edges
(
betweenness
,
S
,
P
,
sigma
,
s
)
;
}
;
var
end_time_b
=
performance
.
now
(
)
;
nodes
.
forEach
(
function
(
s
)
{
delete
betweenness
[
s
]
;
}
)
;
var
result
=
_
.
first
(
_
.
max
(
_
.
pairs
(
betweenness
)
,
_
.
last
)
)
.
split
(
','
)
;
step
.
push
(
result
.
map
(
Number
)
)
;
for
(
var
i
=
0
;
i
<
VirtualAdj
[
result
[
0
]
]
.
length
;
i
++
)
{
if
(
VirtualAdj
[
result
[
0
]
]
[
i
]
.
nei
==
result
[
1
]
||
VirtualAdj
[
result
[
0
]
]
[
i
]
.
ori
==
result
[
1
]
)
{
VirtualAdj
[
result
[
0
]
]
.
splice
(
i
,
1
)
;
break
;
}
}
for
(
var
i
=
0
;
i
<
VirtualAdj
[
result
[
1
]
]
.
length
;
i
++
)
{
if
(
VirtualAdj
[
result
[
1
]
]
[
i
]
.
nei
==
result
[
0
]
||
VirtualAdj
[
result
[
1
]
]
[
i
]
.
ori
==
result
[
0
]
)
{
VirtualAdj
[
result
[
1
]
]
.
splice
(
i
,
1
)
;
break
;
}
}
delete
betweenness
[
_
.
first
(
_
.
max
(
_
.
pairs
(
betweenness
)
,
_
.
last
)
)
]
;
}
console
.
log
(
"Time to run betweenness VS"
)
;
console
.
log
(
end_time_b
-
start_time
)
;
return
step
;
}
function
_single_source_shortest_path_basic_virtual_nodes
(
G
,
s
,
nodes
)
{
var
S
=
[
]
,
P
=
new
Object
(
)
,
sigma
=
new
Object
(
)
,
D
=
new
Object
(
)
;
for
(
i
=
0
;
i
<
G
.
length
;
i
++
)
{
P
[
i
]
=
[
]
;
sigma
[
i
]
=
0
;
D
[
i
]
=
-
1
;
}
sigma
[
s
]
=
1
;
D
[
s
]
=
0
;
var
Q
=
[
]
;
Q
.
push
(
s
)
;
while
(
Q
.
length
>
0
)
{
var
v
=
Q
.
shift
(
)
;
S
.
push
(
v
)
;
for
(
w
=
0
;
w
<
G
[
v
]
.
length
;
w
++
)
{
//G[v].forEach(function (w) {
if
(
D
[
G
[
v
]
[
w
]
.
nei
]
<
0
)
{
Q
.
push
(
G
[
v
]
[
w
]
.
nei
)
;
D
[
G
[
v
]
[
w
]
.
nei
]
=
D
[
v
]
+
1
;
}
if
(
D
[
G
[
v
]
[
w
]
.
nei
]
===
D
[
v
]
+
1
)
{
sigma
[
G
[
v
]
[
w
]
.
nei
]
+=
sigma
[
v
]
;
if
(
nodes
.
indexOf
(
v
)
>=
0
)
{
P
[
G
[
v
]
[
w
]
.
nei
]
.
push
(
v
)
;
}
else
{
P
[
G
[
v
]
[
w
]
.
nei
]
.
push
(
P
[
v
]
)
;
}
}
}
}
return
[
S
,
P
,
sigma
]
;
}
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