====== TQ cores (degrees) ======

[[https://github.com/bavla/TQ/tree/master/Cores|Data for examples]],
[[https://github.com/bavla/Nets/tree/master/source|libraries Nets and TQ]]

The TQ cores algorithm was presented at the Applied Statistics Conference 2016 in Ribno, Slovenia.

<code>
gdir = "c:/users/batagelj/work/python/graph/Nets"
wdir = "C:/Users/batagelj/work/Python/graph/Nets/coresTQ"
import sys, os, json
sys.path = [gdir]+sys.path; os.chdir(wdir)
from Nets import Network as N
from TQ import *
from datetime import datetime

# prLevel = 2 # basic reports
prLevel = 1 # detailed reports
fJSON = 'ExampleA.json'
# fJSON = 'TerrorNews50.json'
# fJSON = "Terror.json"
# fJSON = 'stem.json'

def TQcores(G,prLevel=2):
   D = { u: G.TQnetDeg(u) for u in G._nodes }
   if prLevel<2: print("Deg =",D,"\n")
   Core = { u: [d for d in D[u] if d[2]==0] for u in G.nodes() }
   # core number = 0
   D = { u: [d for d in D[u] if d[2]>0] for u in G.nodes() }
   D = { u: d for u,d in D.items() if d!=[] }
   Dmin = { u: min([e[2] for e in d]) for u,d in D.items() }
   step = 0
   while len(D)>0:
      step += 1
      dmin,u = min( (v,k) for k,v in Dmin.items() )
      if (step % 500 == 1) or (prLevel < 2):
         print("{0:3d}. dmin={1:3d}   node={2:4d}".format(step,dmin,u))
      core = [ d for d in D[u] if d[2] == dmin ]
      Core[u] = TQ.sum(Core[u],core)
      change = TQ.setConst(core,-1)
      D[u] = TQ.cutGE(TQ.sum(D[u],change),dmin)
      if len(D[u])==0: del D[u]; del Dmin[u]
      else: Dmin[u] = min([e[2] for e in D[u]])
      for link in G.star(u):
         v = G.twin(u,link)
         if not(v in D): continue
         chLink = TQ.extract(G.getLink(link,'tq'),change)
         if chLink==[]: continue
         diff = TQ.cutGE(TQ.sum(D[v],chLink),0)
         if len(diff)==0: del D[v]; del Dmin[v]
         else:
            D[v] = TQ.standard([(sd,fd,max(vd,dmin)) for sd,fd,vd in diff])
            Dmin[v] = min([e[2] for e in D[v]])
   print("{0:3d}. dmin={1:3d}   node={2:4d}".format(step,dmin,u))
   return(Core)

G = N.loadNetsJSON(fJSON); G.delLoops()
print("Temporal cores in: ",fJSON)
t1 = datetime.now()
print("started: ",t1.ctime(),"\n")
Core = TQcores(G)
if prLevel<2: print("\n-----\nCore =",Core)
t2 = datetime.now()
print("\nfinished: ",t2.ctime(),"\ntime used: ", t2-t1)
</code>

<code>
>>> 
==== RESTART: C:\Users\batagelj\work\Python\graph\Nets\coresTQ\CoresTQ.py ====
Temporal cores in:  ExampleA.json
started:  Thu Jul  9 01:08:35 2020 

  1. dmin=  1   node=   1
 31. dmin=  3   node=  11

-----
Core = {
   1: [(1, 10, 1)], 
   2: [(1, 2, 2), (2, 5, 3), (5, 10, 2)], 
   3: [(1, 2, 2), (2, 5, 3), (5, 10, 2)], 
   4: [(1, 2, 2), (2, 5, 3), (5, 10, 2)], 
   5: [(1, 2, 2), (2, 5, 3), (5, 10, 2)], 
   6: [(1, 3, 2), (3, 5, 3), (5, 10, 2)], 
   7: [(1, 3, 2), (3, 5, 3), (5, 10, 2)], 
   8: [(1, 3, 2), (3, 5, 3), (5, 10, 2)], 
   9: [(1, 10, 2)], 
  10: [(1, 10, 2)], 
  11: [(1, 3, 2), (3, 5, 3), (5, 10, 2)], 
  12: [(1, 10, 1)], 
  13: [(1, 10, 1)], 
  14: [(1, 4, 1), (4, 6, 2), (6, 10, 1)], 
  15: [(1, 10, 1)], 
  16: [(1, 10, 2)], 
  17: [(1, 10, 2)], 
  18: [(1, 10, 2)], 
  19: [(1, 10, 1)] }

finished:  Thu Jul  9 01:08:36 2020 
time used:  0:00:01.257072
>>> 
</code>


<code>
>>> 
==== RESTART: C:\Users\batagelj\work\Python\graph\Nets\coresTQ\CoresTQ.py ====

network:  exampleB 
 simple violence 
simple= True  directed= True  org= 1  mode= 1  multirel= False  temporal= True 
nodes= 29  links= 176  arcs= 176  edges= 0
Tmin= 1  Tmax= 49
Temporal cores in:  violenceTQ.json
started:  Thu Jul  9 01:34:36 2020 

  1. dmin=  1   node=   1
161. dmin=  5   node=  16

finished:  Thu Jul  9 01:34:37 2020 
time used:  0:00:00.358021
>>> C4 = TQ.TQdictCut(Core,4)
>>> for v in C4:
   print("{0:3d} : {1:11s} ".format(v,G.getNode(v,'lab')),C4[v])
  
  1 : undefined    [(17, 18, 4), (25, 26, 4), (29, 30, 5), (31, 32, 4), (38, 40, 4), (41, 42, 4),
                    (48, 49, 4)]
  2 : ?            [(31, 32, 4), (33, 34, 4)]
  3 : people       [(25, 26, 4), (29, 30, 4), (31, 32, 4), (33, 34, 4), (35, 36, 4), (39, 40, 4), 
                    (41, 42, 4), (48, 49, 4)]
  4 : police       [(17, 18, 4), (29, 30, 5), (31, 32, 4), (33, 34, 4), (35, 36, 4), (39, 40, 4)]
  7 : fascists     [(25, 26, 4), (29, 30, 5), (31, 32, 4), (33, 34, 4), (35, 36, 4), (38, 40, 4), 
                    (41, 42, 4), (48, 49, 4)]
  8 : communists   [(29, 30, 5), (31, 32, 4)]
 10 : socialists   [(17, 18, 4), (29, 30, 4), (35, 36, 4), (39, 40, 4)]
 16 : workers      [(17, 18, 4), (29, 30, 5), (31, 32, 4), (35, 36, 4), (38, 40, 4), (41, 42, 4)]
 17 : the right    [(17, 18, 4)]
 20 : students     [(17, 18, 4)]
 21 : catholics    [(33, 34, 4)]
 25 : republicans  [(31, 32, 4)]
 26 : thugs        [(29, 30, 4)]
>>> 
</code>