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Social Connectome: Unified Frame for Communities and Bursts
- 1. Social Connectome Hang-Hyun Jo Dept. of Physics, Pohang University of Science and Technology, Republic of Korea Dept. of Computer Science, Aalto University School of Science, Finland
- 2. Outline • Mobile phone data for temporal social networks • Community structure and bursty dynamics • Interaction is contextual! • Overlapping communities and contextual bursts • Demographic and geographic analysis • Towards Social Connectome
- 4. Q1: What does the social network look like? Q2: What drives the evolution of the social network? (from a physicist’s viewpoint…)
- 5. A physicist’s viewpoint • More interested in the universal patterns than in the details (But, the devil is in the detail…) • Apply and extend physics to solve the problems derived from social phenomena
- 6. Why mobile phone data? • Mobile phones carried by people almost always • Almost 100% of coverage in many countries • Good proxy of the real social networks
- 7. Mobile phone data • Source: A European operator • Time-resolved call/SMS events among several millions of mobile phone users • Topology = communication network • Dynamics = temporal patterns of communication
- 9. Community structure Onnela et al., PNAS, NJP (2007) A 1 100 10 strong ties in community weak ties between communities
- 10. c~~~~~~~~~~~~~~~~ D AH G D/ C~ A B X E (b) FIG. 2.-Local bridges. a, Degree 3; b, Degree 13. = strong ti weak tie. Strength of weak ties Granovetter, AJS (1973) strong tie weak tie
- 11. Modeling communities Kumpula et al., PRL (2007) global attachment local attachment preferential reinforcement global attachment reset node
- 13. Bursty communication outgoing calls → incoming calls → burst inter-event time τ Karsai et al., PRE (2011) line) Spreading dynamics in the Reality Mining orks (right), for the original event sequence (᭺) W ( ) and DCWB (᭛). In the email network, is directed. The maximum prevalence is limited the SCC and the OUT component (∼85%). tor 2. Similarly for the 100% prevalence 2 (∼342 d), showing that the effects of sistent for the duration of the whole process uns. As for the effect of the random initial all error of mean values in Table I show s (Fig. 1) characterize the overall behavior nitial conditions are demonstrated in Fig. 1, ons are clearly separable at full prevalence. Reality Mining mobile call network and for hown in Fig. 2, with the DCW and DCWB tcome is qualitatively similar with that of ere are certain differences. In the small and , successive calls to many people within a y a hub give rise to a steep prevalence rise. one-off event and the effect is destroyed In the email network, very high-degree uent emails give rise to rapid spreading hed. This effect is conserved in the null y pattern, i.e., variation in overall commu- by the hour, is retained in every null model andomizing the original event sequence. gested that natural periodicities, such as responsible for the fat-tailed waiting time er to evaluate the impact of the daily pattern peed, we carried out simulations where N was used as the network. Events were ks by two Poisson processes that conserve mogeneous Poisson process, and a process s rate follows the daily pattern as calculated cs on hourly basis (see inset in Fig. 3). The h cases are shown in Fig. 3. The difference urves is negligible, demonstrating that the ly a minor impact on the spreading speed. FIG. 3. (Color online) Spreading dynamics as obtained from a Poissonian event-generating model on the aggregated MCN, with daily pattern ( ) and without (᭞). Link weights were taken into account and the curve with the daily pattern is comparable with the DCW null model. Inset: the average daily pattern as observed for the MCN event sequence with binning by the hour. The continuous line is to guide the eye. exclude the possibility that the fat tail in the interevent time distribution is only due to the broad weight distribution as suggested in [21], we calculated the distributions for binned weights and obtained satisfactory scaling with the average interevent time, same as [17]. We find that the distribution can be fitted by a power law with exponent 0.7 over 3.5 decades, followed by a fast decay. The scaling breaks down for small interevent times, where a peak in the distribution at ∼20 s is found, which is due to event correlations between links. The power law indicates non-Poissonian bursty character of the events. Both the characteristics vanish for the time-shuffled null model and the interevent time is well described by an FIG. 4. (Color online) Scaled interevent time distributions for P(⌧) ⇠ ⌧ ↵
- 15. Why? Priority queuing Barabási, Nature (2005) e-mail time priority small waiting time large waiting time waiting time
- 16. Cyclic Poisson process Malmgren et al., PNAS (2008) time-varying rate with weekly cycle for e-mail usage heavy tail of inter-event time distribution Question: Are weekly cycles the ONLY reason for bursts?
- 17. De-seasoning cycles? Jo et al., NJP (2012) mobile call sequence of one user : weekly cycle (T=7 days)⇢(t) : no cyclic patterns⇢⇤ (t⇤ ) = 1 de-seasoned by weekly cycle B7 = 0.146 : burstiness parameter Goh & Barabási, EPL (2008) B0 = 0.224 B = m + m
- 18. Bursts are robust! Burstiness remains finite after de-seasoning weekly cycles. burstiness de-seasoning period (days) different activity group
- 19. strong link weak link Temporal networks time event inter-eventtime
- 20. Social Connectome = a comprehensive map of social interaction Jo (in preparation)
- 21. Social Connectome topological scale dynamicalresolution individual com m unity society aggregate burst seasonality temporal motif layered structure strength of weak ties event egocentric net contextual bursts (CB) circadian cycle overlapping communities (OC) OC+CB
- 22. Unified frame for communities and bursts?
- 23. Triad chain interaction Jo et al., PLOS ONE (2011)
- 24. OR model AND model original without links with w=1
- 25. Figure 2. TI-OR model. A. The cumulative weight distribution Pc(w). B. The average number of next nearest neighbors knn(k). C. The aver overlap O(w). D. The local clustering coefficient c(k). E. The inter-event time distribution P(t). F. The average strength s(k). Results are averaged o 50 realizations for networks with N~5|104 and pML ~10{3 . We obtain SkT&10:1 and ScT&0:08 for pLA ~0:013 and pGA ~0:1. The cases w pLA ~0:1 and/or with pGA ~0:07 are also plotted for comparison. doi:10.1371/journal.pone.0022687.g002 Bursts and Communities in Evolving Networks Figure 3. TI-AND model. A. The cumulative weight distribution Pc(w). B. The av overlap O(w). D. The local clustering coefficient c(k). E. The inter-event time distribu 50 realizations for networks with N~5|104 and pML ~10{3 . We obtain SkT&9:6 an and/or with pGA ~0:04 are also plotted for comparison. doi:10.1371/journal.pone.0022687.g003 Figure 5. Link percolation analysis. A, B. TI-OR model. C, D. TI-AND model. E, F. and the overlap (right panel). For each panel, we calculate the fraction of giant compo as a function of the fraction of removed links, f . Results are averaged over 50 realiz doi:10.1371/journal.pone.0022687.g005 OR model AND model
- 26. Summary • Topology of communication • Granovetter: Strength of weak ties • Kumpula’s model with global/local attachments • Dynamics of communication • Bursts of events
- 27. Not all events are equal. Events are contextual!
- 28. OFFICE HOME MATRIX ??? Jo et al., EPJ DS (2012)
- 29. Time-ordering Figure 11 Time-ordering behavior between services. (a) Distributions of time interval consecutive events of different services s and s′. (b) Diagram for time-ordering behavior bet based on the distributions of time interval. Table 1 k-means clustering results for weekly patterns of service usages Service q = 0 Ns web 74 9 7 6 5 3 3 2 1 1 111 app 50 32 10 7 6 6 5 4 3 1 124 2012, 1:10 Page 13 of 18 nce.com/content/1/1/10 inter-event time between different services/contexts communication services non-communication services
- 30. Context in the topology
- 31. Overlapping community Family Work Alice Bob Family Alice Bob Link communities Work Alice Bob Node communities Spouses Alice and Bob also work togethera b The Alice-Bob link was placed in family but both home and work relationships are identified Ahn et al., Nature (2010) The geo- nly break Fig. 4d, we munity in nity along structures idence for l scale. To ntitatively 103 200 s H+ Threshold, t = 0.20 t = 0.27 0.4 D 0.6 0.8 1 d Largest community Largest subcommunity Remaining hierarchy t e c Word associationMetabolic 0.8 1 Phone Largest community Second largest Third largest mobile phone data
- 32. Multilayer social networks Murase, Jo et al., PRE (2014) AYER WEIGHTED SOCIAL NETWORK MODEL PHYSICAL REVIEW E 90, 052810 (2014) (a) L=1 asc. desc. (b) L=2 asc. desc. 0.2 0.4 0.6 0.8 1 f 0 0.2 0.4 0.6 0.8 1 f 1. (Color online) Link percolation analysis for L = 1 (left) 2 (right). The upper figures show the relative size of the onnected component, RLCC, as a function of the fraction of ved links f . The lower figures show the susceptibility χ. (green dashed) lines correspond to the case when links are (b) p=0.01 (c) p=0.1 (d) p=1 (a) p=0 FIG. 2. (Color) Snapshots of the copy-and-shuffle model with different p shuffling parameter values and N = 300. Red (blue) links are in the first (second) layer, and green links are in both layers. UC MN matic illustration of three kinds of correlated multiplex networks, maximally-positive (MP), uncorrelated (UC), and maximally- f the networks has different types of links, indicated by solid and dashed links, respectively. th permission from Ref. [48]. hysical Society. mple of all possible multilinks in a multiplex network with M = 2 layers and N = 5 nodes. Nodes i and j are linked by one m Ref. [113]. rade layers. Even the two ‘‘negative’’ layers of enmity and attack have significant overlap of the links. Boccaletti et al., Phys. Rep. (2014)
- 33. Context in the dynamics
- 34. decompose! friend A friend B friend C burst contexts burst Contextual bursts Jo et al., PRE (2013) contextual burst
- 35. irrelevant context irrelevant time-frame collective real inter-event time P(l) ⇠ l ↵ contextual real inter-event time P(⌧) ⇠ ⌧ ↵0 contextual ordinal inter-event time P(n) ⇠ n ⌧ = nX i=1 li ↵0 = min{(↵ 1)( 1) + 1, ↵, }
- 36. Returning to the research questions
- 37. Hypothesis: A continuum of overlapping communities Q1: What does the social network look like?
- 38. Q2: What drives the evolution of the social network? Hypothesis: Bursty contextual activities
- 39. Social Connectome topological scale dynamicalresolution individual com m unity society aggregate burst seasonality temporal motif layered structure strength of weak ties event egocentric net contextual bursts (CB) circadian cycle overlapping communities (OC) OC+CB
- 41. Other issues • General framework for stylized facts in social networks [Jo, Murase, Torok, Kaski, Kertesz] • Correlated bursts [Karsai et al., Sci. Rep. (2012); Jo et al., Phys. Rev. E (2015)] • Dynamics on networks: spreading [Jo et al., Phys. Rev. X (2014)] • Perception-based network formation [Jo et al., submitted]
- 42. References • Onnela et al., Proc. Nat. Acad. Sci. USA 104, 7332 (2007); New J. Phys. 9, 179 (2007) • Granovetter, Am. J. Sociol. 78, 1360 (1973) • Kumpula et al., Phys. Rev. Lett. 99, 228701 (2007) • Karsai et al., Phys. Rev. E 83, 025102 (2011) • Barabasi, Nature 435, 207 (2005) • Malmgren et al., Proc. Nat. Acad. Sci. USA 105, 18153 (2008) • Goh & Barabasi, EPL 81, 48002 (2008) • Jo et al., New J. Phys. 14, 013055 (2012) • Jo et al., PLOS ONE 6, e22687 (2011) • Jo et al., EPJ Data Science 1, 10 (2012) • Ahn et al., Nature 466, 761 (2010) • Murase, Jo et al., Phys. Rev. E 90, 052810 (2014) • Jo et al., Phys. Rev. E 87, 062131 (2013) • Jo et al., Phys. Rev. X 4, 011041 (2014)