215:
spread of the contagion to the entire population. Compared to the classic rumour spreading process where nodes are memory-less, link-centric preferential attachment can cause not only a slower spread of the contagion but also one less diffuse. In these models an infected node's chances of connecting to new contacts diminishes as their size of their social circle
214:
Understanding the evolution of a network's structure and how it can influence dynamical processes has become an important part of modeling the spreading of contagions. In models of social and biological contagion spreading on time-varying networks link-centric preferential attachment can alter the
40:
examined this behaviour in the social networks of a group of workers and identified tie strength, a characteristic of social ties describing the frequency of contact between two individuals. From this comes the idea of strong and weak ties, where an individual's strong ties are those she has come
41:
into frequent contact with. Link-centric preferential attachment aims to explain the mechanism behind strong and weak ties as a stochastic reinforcement process for old ties in agent-based modeling where nodes have long-term memory.
190:
121:
235:
grows leading to a limiting effect on the growth of n. The result is strong ties with a node's early contacts and consequently the weakening of the diffusion of the contagion.
206:
More complex models may take into account other variables, such as frequency of contact, contact and intercontact duration, as well as short term memory effects.
233:
67:
36:
In real social networks individuals exhibit a tendency to re-connect with past contacts (ex. family, friends, co-workers, etc.) rather than strangers. In 1970,
69:, the number of contacts it has had in the past. The probability for a node with n social ties to establish a new social tie could then be simply given by
203:(2) = 1/(2 + 1) = 1/3 to create a new tie with D, whereas the probability to reconnect with A or C is twice that at 2/3.
281:
Vestergaard, Christian L.; Genois, Mathieu; Barrat, Alain (October 9, 2014). "How memory generates hetergeneous dynamics in temporal networks".
195:
Figure 1. shows an example of this process: in the first step nodes A and C connect to node B, giving B a total of two social ties. With
708:
49:
In a simple model for this mechanism, a node's propensity to establish a new link can be characterized solely by
703:
25:
136:
75:
651:
596:
498:
426:
361:
342:
Barabasi, Albert-Laszlo; Albert, Reka (October 15, 1999). "Emergence of
Scaling in Random Networks".
300:
21:
403:
Perra, Nicola; Goncalves, Bruno; Pastor-Satorras, Romualdo; Vespignani, Alessandro (June 25, 2012).
620:
586:
559:
488:
416:
385:
351:
324:
290:
20:
is a node's propensity to re-establish links to nodes it has previously been in contact with in
679:
612:
524:
452:
377:
316:
254:
669:
659:
604:
551:
514:
506:
442:
434:
369:
308:
37:
249:
639:
655:
600:
502:
430:
365:
304:
674:
519:
476:
447:
404:
218:
130:
is an offset constant. The probability for a node to re-connect with old ties is then
52:
697:
624:
563:
328:
28:
model relies on nodes keeping memory of previous neighbors up to the current time.
389:
664:
373:
638:
Kamp, Christel; Moslonka-Lefebvre, Mathieu; Alizon, Samuel (December 13, 2013).
608:
312:
577:
Newman, M. E. J. (July 26, 2002). "Spread of epidemic disease on networks".
683:
616:
528:
456:
381:
320:
591:
356:
244:
510:
438:
555:
493:
421:
295:
210:
Effects on the spreading of contagions / weakness of strong ties
542:
Granovetter, Mark (1973). "The strength of weak ties".
477:"Time-varying networks and the weakness of strong ties"
221:
199: = 1, in the next step B has a probability
139:
78:
55:
405:"Activity driven modeling of time-varying networks"
227:
184:
115:
61:
470:
468:
466:
276:
274:
272:
270:
16:In mathematical modeling of social networks,
8:
673:
663:
590:
518:
492:
446:
420:
355:
294:
220:
161:
138:
112:
94:
77:
54:
266:
640:"Epidemic Spread on Weighted Networks"
185:{\displaystyle 1-P(n)={n \over n+c}.}
7:
475:Karsai, Marton (February 10, 2014).
116:{\displaystyle P(n)={c \over n+c}\,}
18:link-centric preferential attachment
14:
155:
149:
88:
82:
1:
544:American Journal of Sociology
665:10.1371/journal.pcbi.1003352
374:10.1126/science.286.5439.509
725:
644:PLOS Computational Biology
609:10.1103/PhysRevE.66.016128
313:10.1103/PhysRevE.90.042805
26:preferential attachment
229:
186:
117:
63:
230:
187:
118:
64:
22:time-varying networks
709:Stochastic processes
219:
137:
76:
53:
656:2013PLSCB...9E3352K
601:2002PhRvE..66a6128N
503:2014NatSR...4E4001K
431:2012NatSR...2E.469P
366:1999Sci...286..509B
305:2014PhRvE..90d2805V
650:(1371): e1003352.
481:Scientific Reports
409:Scientific Reports
225:
182:
113:
59:
585:(16128): 016128.
579:Physical Review E
511:10.1038/srep04001
439:10.1038/srep00469
350:(5439): 509–512.
283:Physical Review E
255:Interpersonal tie
228:{\displaystyle n}
177:
110:
62:{\displaystyle n}
716:
688:
687:
677:
667:
635:
629:
628:
594:
592:cond-mat/0205009
574:
568:
567:
550:(6): 1360–1380.
539:
533:
532:
522:
496:
472:
461:
460:
450:
424:
400:
394:
393:
359:
357:cond-mat/9910332
339:
333:
332:
298:
278:
234:
232:
231:
226:
191:
189:
188:
183:
178:
176:
162:
122:
120:
119:
114:
111:
109:
95:
68:
66:
65:
60:
38:Mark Granovetter
724:
723:
719:
718:
717:
715:
714:
713:
694:
693:
692:
691:
637:
636:
632:
576:
575:
571:
541:
540:
536:
474:
473:
464:
402:
401:
397:
341:
340:
336:
280:
279:
268:
263:
250:Network science
241:
217:
216:
166:
135:
134:
99:
74:
73:
51:
50:
47:
34:
12:
11:
5:
722:
720:
712:
711:
706:
704:Network theory
696:
695:
690:
689:
630:
569:
556:10.1086/225469
534:
462:
395:
334:
265:
264:
262:
259:
258:
257:
252:
247:
240:
237:
224:
193:
192:
181:
175:
172:
169:
165:
160:
157:
154:
151:
148:
145:
142:
124:
123:
108:
105:
102:
98:
93:
90:
87:
84:
81:
58:
46:
43:
33:
30:
13:
10:
9:
6:
4:
3:
2:
721:
710:
707:
705:
702:
701:
699:
685:
681:
676:
671:
666:
661:
657:
653:
649:
645:
641:
634:
631:
626:
622:
618:
614:
610:
606:
602:
598:
593:
588:
584:
580:
573:
570:
565:
561:
557:
553:
549:
545:
538:
535:
530:
526:
521:
516:
512:
508:
504:
500:
495:
490:
486:
482:
478:
471:
469:
467:
463:
458:
454:
449:
444:
440:
436:
432:
428:
423:
418:
414:
410:
406:
399:
396:
391:
387:
383:
379:
375:
371:
367:
363:
358:
353:
349:
345:
338:
335:
330:
326:
322:
318:
314:
310:
306:
302:
297:
292:
289:(4): 042805.
288:
284:
277:
275:
273:
271:
267:
260:
256:
253:
251:
248:
246:
243:
242:
238:
236:
222:
212:
211:
207:
204:
202:
198:
179:
173:
170:
167:
163:
158:
152:
146:
143:
140:
133:
132:
131:
129:
106:
103:
100:
96:
91:
85:
79:
72:
71:
70:
56:
44:
42:
39:
31:
29:
27:
23:
19:
647:
643:
633:
582:
578:
572:
547:
543:
537:
484:
480:
412:
408:
398:
347:
343:
337:
286:
282:
213:
209:
208:
205:
200:
196:
194:
127:
125:
48:
35:
17:
15:
698:Categories
261:References
32:Background
494:1303.5966
422:1203.5351
296:1409.1805
144:−
684:24348225
625:15291065
617:12241447
564:59578641
529:24510159
487:: 4001.
457:22741058
382:10521342
329:16022001
321:25375547
245:BA model
239:See also
45:Examples
675:3861041
652:Bibcode
597:Bibcode
520:3918922
499:Bibcode
448:3384079
427:Bibcode
415:: 469.
362:Bibcode
344:Science
301:Bibcode
24:. This
682:
672:
623:
615:
562:
527:
517:
455:
445:
390:524106
388:
380:
327:
319:
126:where
621:S2CID
587:arXiv
560:S2CID
489:arXiv
417:arXiv
386:S2CID
352:arXiv
325:S2CID
291:arXiv
680:PMID
613:PMID
525:PMID
453:PMID
378:PMID
317:PMID
670:PMC
660:doi
605:doi
552:doi
515:PMC
507:doi
443:PMC
435:doi
370:doi
348:286
309:doi
700::
678:.
668:.
658:.
646:.
642:.
619:.
611:.
603:.
595:.
583:66
581:.
558:.
548:78
546:.
523:.
513:.
505:.
497:.
483:.
479:.
465:^
451:.
441:.
433:.
425:.
411:.
407:.
384:.
376:.
368:.
360:.
346:.
323:.
315:.
307:.
299:.
287:90
285:.
269:^
686:.
662::
654::
648:9
627:.
607::
599::
589::
566:.
554::
531:.
509::
501::
491::
485:4
459:.
437::
429::
419::
413:2
392:.
372::
364::
354::
331:.
311::
303::
293::
223:n
201:P
197:c
180:.
174:c
171:+
168:n
164:n
159:=
156:)
153:n
150:(
147:P
141:1
128:c
107:c
104:+
101:n
97:c
92:=
89:)
86:n
83:(
80:P
57:n
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.