### DATA 620: HW3

##### Daina Bouquin

Dataset:
The file astro-ph.gml contains the collaboration network of scientists posting preprints on the astrophysics archive at www.arxiv.org, 1995-1999, as compiled by M. Newman.

``````

In [27]:

import networkx as nx
import pylab as plt # for plotting

``````
``````

In [4]:

``````
``````

In [7]:

H # verify that the data has been read in

``````
``````

Out[7]:

<networkx.classes.graph.Graph at 0x105c36690>

``````
``````

In [12]:

print "Nodes:", H.number_of_nodes()
print "Edges:", H.number_of_edges()

``````
``````

Nodes: 16706
Edges: 121251

``````
``````

In [17]:

# draw the network
%matplotlib inline
nx.draw(H) # Well, that isn't very useful...

``````
``````

``````
``````

In [121]:

#Create small subgraph (first 20 nodes) just for graphing demo
Hsub = H.subgraph([0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19])
nx.draw_random(Hsub)

``````
``````

``````
``````

In [122]:

# Degree centrality (valency) of a node of a graph:
# the fraction of nodes a node v is connected to
nx.degree(H)

``````
``````

Out[122]:

{0: 36,
1: 1,
2: 5,
3: 4,
4: 16,
5: 17,
6: 47,
7: 12,
8: 2,
9: 2,
10: 17,
11: 3,
12: 70,
13: 3,
14: 13,
15: 3,
16: 7,
17: 33,
18: 26,
19: 72,
20: 111,
21: 51,
22: 4,
23: 24,
24: 2,
25: 6,
26: 3,
27: 2,
28: 23,
29: 5,
30: 67,
31: 32,
32: 15,
33: 2,
34: 2,
35: 2,
36: 32,
37: 11,
38: 2,
39: 62,
40: 22,
41: 38,
42: 51,
43: 24,
44: 105,
45: 54,
46: 14,
47: 2,
48: 2,
49: 1,
50: 13,
51: 15,
52: 17,
53: 17,
54: 27,
55: 103,
56: 14,
57: 1,
58: 6,
59: 7,
60: 43,
61: 81,
62: 22,
63: 32,
64: 21,
65: 29,
66: 71,
67: 7,
68: 6,
69: 20,
70: 38,
71: 26,
72: 4,
73: 2,
74: 2,
75: 2,
76: 31,
77: 45,
78: 10,
79: 65,
80: 42,
81: 7,
82: 22,
83: 12,
84: 52,
85: 7,
86: 10,
87: 16,
88: 3,
89: 42,
90: 4,
91: 8,
92: 15,
93: 151,
94: 1,
95: 8,
96: 27,
97: 8,
98: 31,
99: 1,
100: 21,
101: 1,
102: 1,
103: 84,
104: 36,
105: 101,
106: 3,
107: 21,
108: 3,
109: 7,
110: 9,
111: 8,
112: 6,
113: 41,
114: 4,
115: 29,
116: 10,
117: 94,
118: 5,
119: 6,
120: 2,
121: 0,
122: 1,
123: 1,
124: 0,
125: 79,
126: 10,
127: 22,
128: 95,
129: 95,
130: 20,
131: 31,
132: 89,
133: 17,
134: 26,
135: 49,
136: 28,
137: 22,
138: 13,
139: 6,
140: 27,
141: 6,
142: 12,
143: 18,
144: 2,
145: 2,
146: 26,
147: 18,
148: 66,
149: 11,
150: 9,
151: 48,
152: 8,
153: 1,
154: 12,
155: 7,
156: 11,
157: 14,
158: 2,
159: 2,
160: 44,
161: 1,
162: 11,
163: 20,
164: 13,
165: 68,
166: 31,
167: 2,
168: 13,
169: 44,
170: 21,
171: 75,
172: 13,
173: 6,
174: 23,
175: 23,
176: 16,
177: 4,
178: 22,
179: 2,
180: 2,
181: 11,
182: 14,
183: 4,
184: 8,
185: 6,
186: 7,
187: 9,
188: 3,
189: 6,
190: 7,
191: 3,
192: 24,
193: 40,
194: 10,
195: 9,
196: 6,
197: 1,
198: 22,
199: 11,
200: 5,
201: 2,
202: 35,
203: 38,
204: 12,
205: 106,
206: 100,
207: 100,
208: 124,
209: 114,
210: 181,
211: 125,
212: 37,
213: 106,
214: 105,
215: 48,
216: 107,
217: 215,
218: 103,
219: 110,
220: 94,
221: 106,
222: 173,
223: 57,
224: 41,
225: 37,
226: 48,
227: 70,
228: 2,
229: 1,
230: 181,
231: 166,
232: 104,
233: 8,
234: 46,
235: 126,
236: 74,
237: 54,
238: 73,
239: 4,
240: 2,
241: 2,
242: 4,
243: 32,
244: 64,
245: 14,
246: 57,
247: 11,
248: 8,
249: 30,
250: 20,
251: 19,
252: 10,
253: 40,
254: 8,
255: 76,
256: 4,
257: 51,
258: 19,
259: 1,
260: 104,
261: 28,
262: 28,
263: 39,
264: 104,
265: 7,
266: 12,
267: 14,
268: 117,
269: 12,
270: 7,
271: 2,
272: 41,
273: 8,
274: 8,
275: 17,
276: 5,
277: 0,
278: 19,
279: 7,
280: 38,
281: 29,
282: 4,
283: 9,
284: 23,
285: 6,
286: 5,
287: 1,
288: 3,
289: 3,
290: 3,
291: 2,
292: 3,
293: 5,
294: 11,
295: 4,
296: 7,
297: 1,
298: 1,
299: 12,
300: 15,
301: 1,
302: 1,
303: 7,
304: 4,
305: 79,
306: 14,
307: 4,
308: 4,
309: 14,
310: 4,
311: 8,
312: 4,
313: 12,
314: 6,
315: 4,
316: 20,
317: 9,
318: 7,
319: 6,
320: 10,
321: 14,
322: 0,
323: 4,
324: 10,
325: 6,
326: 64,
327: 4,
328: 2,
329: 2,
330: 17,
331: 15,
332: 50,
333: 45,
334: 156,
335: 33,
336: 56,
337: 2,
338: 4,
339: 13,
340: 6,
341: 2,
342: 18,
343: 8,
344: 14,
345: 55,
346: 67,
347: 36,
348: 23,
349: 21,
350: 19,
351: 25,
352: 60,
353: 1,
354: 21,
355: 34,
356: 71,
357: 10,
358: 10,
359: 78,
360: 8,
361: 5,
362: 2,
363: 27,
364: 2,
365: 9,
366: 7,
367: 2,
368: 89,
369: 67,
370: 61,
371: 40,
372: 19,
373: 52,
374: 3,
375: 3,
376: 3,
377: 3,
378: 20,
379: 19,
380: 21,
381: 2,
382: 30,
383: 31,
384: 40,
385: 39,
386: 11,
387: 16,
388: 0,
389: 63,
390: 51,
391: 43,
392: 28,
393: 16,
394: 36,
395: 142,
396: 61,
397: 56,
398: 73,
399: 72,
400: 15,
401: 2,
402: 4,
403: 45,
404: 3,
405: 20,
406: 6,
407: 74,
408: 65,
409: 1,
410: 4,
411: 1,
412: 9,
413: 8,
414: 33,
415: 12,
416: 5,
417: 20,
418: 5,
419: 28,
420: 10,
421: 11,
422: 13,
423: 37,
424: 13,
425: 5,
426: 10,
427: 0,
428: 1,
429: 4,
430: 2,
431: 12,
432: 10,
433: 15,
434: 15,
435: 188,
436: 13,
437: 6,
438: 22,
439: 10,
440: 0,
441: 22,
442: 30,
443: 33,
444: 0,
445: 14,
446: 12,
447: 9,
448: 17,
449: 9,
450: 9,
451: 4,
452: 36,
453: 8,
454: 9,
455: 38,
456: 22,
457: 17,
458: 43,
459: 27,
460: 27,
461: 1,
462: 1,
463: 32,
464: 14,
465: 43,
466: 10,
467: 81,
468: 193,
469: 34,
470: 50,
471: 55,
472: 65,
473: 12,
474: 4,
475: 26,
476: 3,
477: 9,
478: 2,
479: 19,
480: 77,
481: 15,
482: 10,
483: 10,
484: 146,
485: 147,
486: 40,
487: 18,
488: 24,
489: 11,
490: 56,
491: 2,
492: 24,
493: 42,
494: 2,
495: 1,
496: 25,
497: 144,
498: 2,
499: 49,
500: 36,
501: 12,
502: 7,
503: 21,
504: 17,
505: 3,
506: 3,
507: 3,
508: 3,
509: 29,
510: 19,
511: 30,
512: 41,
513: 12,
514: 3,
515: 18,
516: 104,
517: 73,
518: 36,
519: 34,
520: 42,
521: 19,
522: 2,
523: 28,
524: 16,
525: 10,
526: 3,
527: 18,
528: 46,
529: 8,
530: 41,
531: 9,
532: 9,
533: 7,
534: 144,
535: 17,
536: 67,
537: 16,
538: 57,
539: 18,
540: 16,
541: 16,
542: 16,
543: 4,
544: 70,
545: 1,
546: 10,
547: 5,
548: 25,
549: 0,
550: 2,
551: 0,
552: 4,
553: 4,
554: 4,
555: 19,
556: 4,
557: 12,
558: 0,
559: 37,
560: 7,
561: 18,
562: 2,
563: 3,
564: 5,
565: 23,
566: 4,
567: 3,
568: 14,
569: 4,
570: 69,
571: 2,
572: 54,
573: 8,
574: 21,
575: 22,
576: 4,
577: 16,
578: 8,
579: 32,
580: 26,
581: 152,
582: 4,
583: 37,
584: 4,
585: 24,
586: 3,
587: 3,
588: 4,
589: 1,
590: 34,
591: 42,
592: 0,
593: 22,
594: 20,
595: 18,
596: 24,
597: 115,
598: 22,
599: 53,
600: 28,
601: 13,
602: 27,
603: 40,
604: 49,
605: 36,
606: 33,
607: 33,
608: 33,
609: 36,
610: 34,
611: 33,
612: 33,
613: 33,
614: 48,
615: 33,
616: 48,
617: 33,
618: 40,
619: 33,
620: 33,
621: 38,
622: 27,
623: 33,
624: 38,
625: 34,
626: 33,
627: 42,
628: 33,
629: 33,
630: 1,
631: 50,
632: 8,
633: 33,
634: 35,
635: 54,
636: 6,
637: 100,
638: 6,
639: 21,
640: 9,
641: 11,
642: 8,
643: 60,
644: 2,
645: 2,
646: 59,
647: 33,
648: 27,
649: 30,
650: 14,
651: 26,
652: 5,
653: 10,
654: 13,
655: 26,
656: 30,
657: 29,
658: 31,
659: 10,
660: 36,
661: 21,
662: 9,
663: 16,
664: 34,
665: 24,
666: 78,
667: 25,
668: 9,
669: 27,
670: 11,
671: 2,
672: 4,
673: 3,
674: 37,
675: 6,
676: 1,
677: 2,
678: 15,
679: 13,
680: 23,
681: 18,
682: 31,
683: 16,
684: 8,
685: 5,
686: 5,
687: 48,
688: 6,
689: 6,
690: 2,
691: 4,
692: 18,
693: 3,
694: 15,
695: 11,
696: 33,
697: 67,
698: 35,
699: 16,
700: 2,
701: 13,
702: 3,
703: 2,
704: 43,
705: 6,
706: 8,
707: 6,
708: 6,
709: 5,
710: 62,
711: 107,
712: 0,
713: 13,
714: 47,
715: 3,
716: 47,
717: 1,
718: 7,
719: 40,
720: 1,
721: 41,
722: 147,
723: 99,
724: 5,
725: 72,
726: 40,
727: 31,
728: 12,
729: 37,
730: 17,
731: 34,
732: 25,
733: 3,
734: 1,
735: 84,
736: 123,
737: 16,
738: 4,
739: 15,
740: 10,
741: 10,
742: 2,
743: 0,
744: 30,
745: 10,
746: 11,
747: 181,
748: 11,
749: 6,
750: 11,
751: 39,
752: 1,
753: 15,
754: 11,
755: 15,
756: 11,
757: 11,
758: 17,
759: 27,
760: 11,
761: 11,
762: 11,
763: 11,
764: 20,
765: 7,
766: 4,
767: 4,
768: 67,
769: 3,
770: 11,
771: 15,
772: 2,
773: 5,
774: 22,
775: 40,
776: 17,
777: 24,
778: 128,
779: 0,
780: 8,
781: 3,
782: 51,
783: 15,
784: 9,
785: 11,
786: 26,
787: 8,
788: 1,
789: 1,
790: 20,
791: 42,
792: 21,
793: 49,
794: 21,
795: 30,
796: 117,
797: 3,
798: 42,
799: 14,
800: 29,
801: 38,
802: 18,
803: 39,
804: 4,
805: 7,
806: 3,
807: 9,
808: 40,
809: 37,
810: 8,
811: 15,
812: 6,
813: 14,
814: 6,
815: 31,
816: 43,
817: 78,
818: 0,
819: 10,
820: 35,
821: 17,
822: 13,
823: 8,
824: 17,
825: 4,
826: 35,
827: 39,
828: 20,
829: 11,
830: 23,
831: 33,
832: 39,
833: 17,
834: 127,
835: 11,
836: 22,
837: 60,
838: 5,
839: 5,
840: 9,
841: 13,
842: 13,
843: 30,
844: 50,
845: 11,
846: 28,
847: 81,
848: 8,
849: 9,
850: 4,
851: 8,
852: 14,
853: 0,
854: 0,
855: 3,
856: 11,
857: 15,
858: 4,
859: 11,
860: 20,
861: 8,
862: 2,
863: 49,
864: 16,
865: 24,
866: 4,
867: 5,
868: 13,
869: 2,
870: 26,
871: 2,
872: 7,
873: 2,
874: 6,
875: 1,
876: 5,
877: 1,
878: 1,
879: 39,
880: 3,
881: 2,
882: 2,
883: 4,
884: 1,
885: 1,
886: 4,
887: 4,
888: 31,
889: 8,
890: 15,
891: 9,
892: 3,
893: 8,
894: 1,
895: 33,
896: 3,
897: 66,
898: 15,
899: 2,
900: 0,
901: 70,
902: 2,
903: 84,
904: 15,
905: 9,
906: 6,
907: 11,
908: 9,
909: 6,
910: 6,
911: 19,
912: 353,
913: 73,
914: 9,
915: 13,
916: 45,
917: 18,
918: 14,
919: 12,
920: 4,
921: 9,
922: 2,
923: 5,
924: 13,
925: 48,
926: 24,
927: 30,
928: 45,
929: 1,
930: 112,
931: 2,
932: 1,
933: 3,
934: 0,
935: 6,
936: 21,
937: 7,
938: 6,
939: 8,
940: 12,
941: 32,
942: 35,
943: 7,
944: 54,
945: 19,
946: 67,
947: 10,
948: 19,
949: 3,
950: 2,
951: 23,
952: 17,
953: 24,
954: 33,
955: 5,
956: 3,
957: 6,
958: 67,
959: 94,
960: 51,
961: 24,
962: 24,
963: 44,
964: 23,
965: 30,
966: 23,
967: 51,
968: 38,
969: 24,
970: 30,
971: 26,
972: 24,
973: 58,
974: 19,
975: 19,
976: 27,
977: 26,
978: 36,
979: 65,
980: 19,
981: 20,
982: 28,
983: 37,
984: 0,
985: 10,
986: 19,
987: 7,
988: 10,
989: 20,
990: 11,
991: 9,
992: 1,
993: 9,
994: 8,
995: 7,
996: 6,
997: 12,
998: 46,
999: 45,
...}

``````
``````

In [87]:

# Looking to find diameter, hit issue with disconnected graph
nx.is_connected(H)

``````
``````

Out[87]:

False

``````
``````

In [99]:

# Create list of connected graphs
Gcc = nx.connected_component_subgraphs(H)

``````
``````

In [102]:

# Find number of nodes for each connected graph
[len(g) for g in Gcc] # the first and largest is most important

``````
``````

Out[102]:

[14845,
3,
7,
2,
1,
2,
1,
1,
2,
4,
2,
2,
1,
4,
1,
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14,
1,
1,
1,
1,
1,
1,
1,
2,
1,
1,
6,
1,
1,
1,
2,
2,
1,
1,
4,
1,
1,
1,
1,
1,
5,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
6,
5,
1,
3,
3,
2,
4,
4,
1,
2,
2,
2,
1,
3,
1,
3,
3,
4,
5,
1,
2,
1,
1,
1,
19,
1,
1,
2,
1,
3,
1,
1,
3,
1,
1,
1,
2,
1,
1,
2,
3,
3,
1,
1,
2,
2,
1,
1,
1,
1,
1,
4,
1,
1,
1,
3,
2,
2,
3,
1,
2,
1,
1,
1,
3,
1,
1,
3,
1,
1,
1,
1,
1,
1,
1,
2,
8,
1,
2,
1,
1,
2,
1,
2,
3,
1,
1,
5,
5,
2,
1,
1,
1,
1,
1,
1,
1,
6,
1,
1,
1,
1,
4,
1,
15,
2,
4,
1,
1,
2,
2,
3,
1,
1,
2,
1,
1,
1,
3,
1,
3,
1,
2,
2,
4,
2,
1,
1,
1,
5,
1,
1,
1,
1,
3,
3,
1,
1,
1,
1,
1,
1,
2,
5,
1,
1,
1,
2,
3,
4,
2,
4,
1,
1,
2,
1,
1,
1,
1,
1,
3,
1,
1,
1,
1,
3,
3,
3,
1,
1,
1,
1,
1,
1,
1,
3,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
1,
1,
1,
2,
1,
1,
3,
3,
3,
2,
3,
2,
3,
2,
1,
1,
2,
2,
3,
1,
1,
1,
3,
3,
1,
3,
1,
1,
1,
1,
2,
1,
2,
2,
2,
1,
1,
2,
1,
4,
1,
1,
4,
1,
1,
2,
1,
1,
1,
1,
2,
2,
1,
1,
2,
1,
1,
1,
1,
2,
1,
1,
1,
2,
2,
1,
1,
1,
1,
1,
2,
1,
1,
4,
2,
1,
2,
1,
2,
1,
1,
1,
2,
1,
2,
3,
1,
1,
1,
1,
1,
4,
6,
1,
1,
1,
1,
1,
1,
2,
3,
1,
1,
1,
4,
1,
1,
6,
1,
1,
1,
6,
1,
1,
4,
2,
1,
1,
2,
1,
1,
1,
3,
1,
2,
3,
1,
1,
1,
1,
1,
1,
1,
2,
1,
1,
1,
3,
4,
2,
1,
1,
1,
1,
1,
4,
1,
2,
1,
2,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
4,
1,
1,
4,
1,
1,
1,
2,
1,
1,
1,
1,
2,
1,
1,
2,
1,
1,
1,
1,
1,
4,
2,
1,
1,
1,
3,
1,
1,
1,
2,
1,
1,
1,
2,
1,
1,
2,
2,
1,
3,
1,
3,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
1,
1,
3,
1,
2,
3,
1,
1,
2,
1,
2,
3,
3,
1,
1,
3,
4,
3,
3,
1,
2,
1,
1,
1,
6,
2,
1,
1,
1,
2,
1,
1,
1,
1,
1,
1,
1,
1,
3,
1,
1,
1,
1,
1,
2,
1,
2,
1,
1,
1,
1,
2,
4,
1,
2,
1,
1,
1,
1,
1,
4,
1,
1,
1,
3,
1,
1,
5,
1,
1,
1,
1,
1,
1,
1,
1,
1,
4,
1,
3,
1,
1,
1,
1,
1,
2,
1,
1,
2,
1,
1,
3,
2,
1,
1,
2,
1,
1,
1,
9,
1,
2,
1,
1,
1,
2,
2,
1,
6,
3,
1,
3,
1,
1,
1,
1,
1,
1,
3,
1,
1,
5,
1,
1,
6,
1,
3,
1,
2,
1,
1,
1,
7,
1,
1,
1,
1,
1,
1,
4,
5,
1,
2,
2,
1,
1,
1,
1,
1,
2,
7,
1,
1,
1,
1,
1,
2,
3,
1,
1,
1,
4,
1,
3,
1,
2,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
2,
1,
1,
1,
...]

``````
``````

In [117]:

# Show all of the connected components
sorted(nx.connected_components(H))

``````
``````

Out[117]:

[[0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
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13,
14,
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17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45,
46,
47,
48,
49,
50,
51,
52,
53,
54,
55,
56,
59,
60,
61,
62,
63,
64,
65,
66,
67,
68,
69,
70,
71,
72,
73,
74,
75,
76,
77,
78,
79,
80,
81,
82,
83,
84,
85,
86,
87,
88,
89,
90,
91,
92,
93,
94,
95,
96,
97,
98,
99,
100,
103,
104,
105,
106,
107,
108,
109,
110,
111,
112,
113,
114,
115,
116,
117,
118,
119,
120,
125,
126,
127,
128,
129,
130,
131,
132,
133,
134,
135,
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137,
138,
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141,
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148,
149,
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155,
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162,
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182,
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206,
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210,
211,
212,
213,
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215,
216,
217,
218,
219,
220,
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222,
223,
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226,
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231,
232,
233,
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239,
240,
241,
242,
243,
244,
245,
246,
247,
248,
249,
250,
251,
252,
253,
254,
255,
256,
257,
258,
259,
260,
261,
262,
263,
264,
265,
266,
267,
268,
269,
270,
271,
272,
273,
274,
275,
276,
278,
279,
280,
281,
282,
283,
284,
285,
286,
290,
291,
292,
293,
294,
295,
296,
299,
300,
303,
304,
305,
306,
307,
308,
309,
310,
311,
312,
313,
314,
315,
316,
317,
318,
319,
320,
321,
323,
324,
325,
326,
327,
328,
329,
330,
331,
332,
333,
334,
335,
336,
337,
338,
339,
340,
341,
342,
343,
344,
345,
346,
347,
348,
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351,
352,
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360,
361,
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371,
372,
373,
378,
379,
380,
381,
382,
383,
384,
385,
386,
387,
389,
390,
391,
392,
393,
394,
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396,
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398,
399,
400,
401,
402,
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405,
406,
407,
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409,
410,
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414,
415,
416,
417,
418,
419,
420,
421,
422,
423,
424,
425,
426,
428,
429,
430,
431,
432,
433,
434,
435,
436,
437,
438,
439,
441,
442,
443,
445,
446,
447,
448,
449,
450,
451,
452,
453,
454,
455,
456,
457,
458,
459,
460,
463,
464,
465,
466,
467,
468,
469,
470,
471,
472,
473,
474,
475,
476,
477,
478,
479,
480,
481,
482,
483,
484,
485,
486,
487,
488,
489,
490,
491,
492,
493,
494,
495,
496,
497,
498,
499,
500,
501,
502,
503,
504,
509,
510,
511,
512,
513,
514,
515,
516,
517,
518,
519,
520,
521,
522,
523,
524,
525,
526,
527,
528,
529,
530,
531,
532,
533,
534,
535,
536,
537,
538,
539,
540,
541,
542,
543,
544,
545,
546,
547,
548,
552,
553,
554,
555,
556,
557,
559,
560,
561,
562,
563,
564,
565,
566,
567,
568,
569,
570,
571,
572,
573,
574,
575,
576,
577,
578,
579,
580,
581,
582,
583,
584,
585,
586,
587,
588,
589,
590,
591,
593,
594,
595,
596,
597,
598,
599,
600,
601,
602,
603,
604,
605,
606,
607,
608,
609,
610,
611,
612,
613,
614,
615,
616,
617,
618,
619,
620,
621,
622,
623,
624,
625,
626,
627,
628,
629,
630,
631,
632,
633,
634,
635,
636,
637,
638,
639,
640,
641,
642,
643,
644,
645,
646,
647,
648,
649,
650,
651,
652,
653,
654,
655,
656,
657,
658,
659,
660,
661,
662,
663,
664,
665,
666,
667,
668,
669,
670,
671,
672,
673,
674,
675,
676,
677,
678,
679,
680,
681,
682,
683,
684,
685,
686,
687,
688,
689,
690,
691,
692,
693,
694,
695,
696,
697,
698,
699,
700,
701,
702,
703,
704,
705,
706,
707,
708,
709,
710,
711,
713,
714,
715,
716,
717,
718,
719,
720,
721,
722,
723,
724,
725,
726,
727,
728,
729,
730,
731,
732,
733,
734,
735,
736,
737,
738,
739,
740,
741,
742,
744,
745,
746,
747,
748,
749,
750,
751,
752,
753,
754,
755,
756,
757,
758,
759,
760,
761,
762,
763,
764,
765,
766,
767,
768,
769,
770,
771,
772,
773,
774,
775,
776,
777,
778,
780,
781,
782,
783,
784,
785,
786,
787,
790,
791,
792,
793,
794,
795,
796,
797,
798,
799,
800,
801,
802,
803,
804,
805,
806,
807,
808,
809,
810,
811,
812,
813,
814,
815,
816,
817,
819,
820,
821,
822,
823,
824,
825,
826,
827,
828,
829,
830,
831,
832,
833,
834,
835,
836,
837,
838,
839,
840,
841,
842,
843,
844,
845,
846,
847,
848,
849,
850,
851,
852,
855,
856,
857,
858,
859,
860,
861,
862,
863,
864,
865,
866,
867,
868,
869,
870,
871,
872,
873,
874,
875,
876,
879,
880,
881,
882,
883,
886,
887,
888,
889,
890,
891,
892,
893,
894,
895,
896,
897,
898,
899,
901,
902,
903,
904,
905,
906,
907,
908,
909,
910,
911,
912,
913,
914,
915,
916,
917,
918,
919,
920,
921,
922,
923,
924,
925,
926,
927,
928,
930,
931,
933,
935,
936,
937,
938,
939,
940,
941,
942,
943,
944,
945,
946,
947,
948,
949,
950,
951,
952,
953,
954,
955,
957,
958,
959,
960,
961,
962,
963,
964,
965,
966,
967,
968,
969,
970,
971,
972,
973,
974,
975,
976,
977,
978,
979,
980,
981,
982,
983,
985,
986,
987,
988,
989,
990,
991,
992,
993,
994,
995,
996,
997,
998,
999,
1000,
1001,
1002,
1003,
1004,
1005,
1006,
1007,
1008,
1009,
1010,
1011,
1012,
1013,
1014,
1015,
1016,
1017,
1018,
1019,
1020,
1021,
1022,
1023,
1024,
1025,
1026,
1027,
1028,
1029,
1030,
1031,
1032,
1033,
1034,
1035,
1036,
1037,
1038,
1039,
1040,
1041,
1042,
1043,
1044,
1045,
1046,
1047,
1048,
1049,
1050,
1051,
1052,
1053,
1054,
1055,
1056,
...],
[33, 34, 35],
[101, 102],
[121],
[122, 123],
[124],
[277],
[288, 289, 3066, 3067],
[297, 298],
[301, 302],
[322],
[376, 377, 374, 375],
[388],
[427],
[440],
[444],
[461, 462],
[505, 506, 507, 508],
[549],
[551],
[558],
[592],
[712],
[743],
[779],
[788, 789],
[818],
[853],
[854],
[877, 878],
[884, 885],
[900],
[929, 1439],
[934],
[984],
[1058],
[1066, 1067],
[1088],
[1114, 1115],
[1130],
[1132, 1133],
[1171],
[1172],
[1215],
[1223],
[1229, 1230],
[1269],
[1284],
[1302],
[1303],
[1313],
[1349],
[1355],
[1384, 8520, 8521, 1383],
[1387, 1388, 12197],
[1404],
[1416, 1417, 1418],
[1419, 1420, 1421],
[1434, 1435],
[1438],
[1447],
[1496],
[1515],
[1555, 1556],
[1634],
[1640, 1641, 1638, 1639],
[1650, 1651, 1652, 1653],
[1659],
[1707, 1708, 11255],
[1728],
[1729],
[1731, 1732],
[1785],
[1806],
[1816, 1817, 1818, 1819],
[1832, 1833],
[1837, 1838],
[1864, 1863],
[1944],
[1955],
[2012, 2013, 2014],
[2042],
[2058],
[2059],
[2061],
[2062],
[2064],
[2071],
[2074],
[2076],
[2100],
[2101],
[2109],
[2131],
[2132],
[2171],
[2249],
[2256, 2257, 15581],
[2297],
[2307],
[2313],
[2342],
[2431],
[2456, 2457, 2458, 2455],
[2468],
[2524],
[2525, 2526],
[2579],
[2580],
[2619],
[2628],
[2629],
[2633, 2634],
[2645],
[2654],
[2672, 2673, 2674, 9629],
[2694],
[2801, 2802, 2803],
[2806],
[2832, 2833, 2834, 2835],
[2851],
[2859],
[2861, 2862, 2863],
[2897],
[3021, 3967],
[3022],
[3026],
[3037],
[3051],
[3186, 3187, 9837],
[3201],
[3203, 932],
[3209, 3210],
[3260],
[3282],
[3290, 3291, 6514],
[3304, 3305, 5421, 3302, 3303],
[3318],
[3324, 3325, 3326, 3327],
[3392],
[3408],
[3422],
[3453, 3454, 3455],
[3477],
[3480, 3481, 9348],
[3524, 3525],
[3538],
[3556],
[3589],
[3627],
[3630, 3631],
[3675, 3676],
[3717],
[3733],
[3749],
[3784],
[3785, 3786],
[3787],
[3791],
[3793, 3794],
[3795],
[3800, 3801, 3802],
[3803, 3804],
[3829],
[3855],
[3856],
[3857],
[3858],
[3869, 3870],
[3872, 11092, 3871],
[3892],
[3900],
[3906],
[3927],
[3933],
[3949],
[3957, 3958],
[3965, 3966],
[3972],
[3973],
[4011],
[4041, 4042, 4043, 4044, 9518, 9519, 9520, 15063],
[4062],
[4102],
[4154],
[4156, 4157, 4158, 5621],
[4171, 4172, 4173],
[4181],
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[16518],
...]

``````

### Analysis with Gephi:

I was able to calculate the diameter of the complete graph (maximum eccentricity of any vertex in the graph/greatest distance between any pair of vertices) despite disconnection issues, and average path length of the network using Gephi: