Familiar Strangers: the Collective Regularity inHuman Behaviors

Yan LengMIT Media Lab

Cambridge, MA, USAEmail: yleng@mit.edu

Dominiquo SantistevanElectrical Engineering & Computer Science

Cambridge, MA, USAEmail: niquo@mit.edu

Alex ’Sandy’ PentlandMIT Media Lab

Cambridge, MA, USAEmail: pentland@mit.edu

Abstract—The social phenomenon of familiar strangers wasidentified by Stanley Milgram in 1972 with a small-scale ex-periment. However, there has been limited research focusing onuncovering the phenomenon at a societal scale and simultaneouslyinvestigating the social relationships between familiar strangers.With the help of the large-scale mobile phone records, weempirically show the existence of the relationship in the countryof Andorra. Built upon the temporal and spatial distributions,we investigate the mechanisms, especially collective temporalregularity and spatial structure that trigger this phenomenon.Moreover, we explore the relationship between social distanceson the communication network and the number of encountersand show that larger number of encounters indicates shortersocial distances in a social network. The understanding of thephysical encounter network could have important implicationsto understand the phenomena such as epidemics spreading andinformation diffusion.

It is a common phenomenon to encounter strangers duringregular activities in our daily lives whom we can recognizebut never formally interact with [1], [2]. This intriguing socialphenomenon of ”Familiar Stranger” of the urban environment,first identified by Stanley Milgram in 1972 by asking travelersto recognize ”strangers” they met on a bus platform [1]. In2013, Sun [3], for the first time, uncovered the encountermechanisms of three million public transit users in Singaporeto capture the time-resolved, in-vehicle encounter patterns andfamiliar strangers using transit smart-card data.

This hidden dynamic social network plays an unnoticeablebut significant role in information diffusion, behavior syn-chronization, and epidemics spreading process. Christakis [4]and Montanari [5] shed light on the diffusion of information,innovations and behaviors via social contagion driven by socialinteractions. Dong used a Markov jump process to capture theco-evolution of friendship and visitation patterns in a studentdorms with monthly surveys and locations tracking throughmobile phones [6]. Besides, a series of studies have focusedon using large-scale or high-resolution data to empiricallyand computationally model the epidemics process. Danonshowed that large-scale interaction data are needed to verifythe assumptions of random transmission models and simplenetwork structures to understand better and predict the diseasetransmission [7]. Stopczynski utilized large-scale behavioraldata for modeling epidemic prediction by physical proximitynetwork [8]. Isella and Salathe tracked high-resolution prox-imity network to understand the transmission paths of diseases[9], [10].

To capture the physical proximity network in the urban

environment, we use countrywide mobile phone logs to ex-plore the phenomenon and underlying mechanisms that triggerfamiliar strangers on a societal scale covering many aspectsof social lives. This data simultaneously captures two layersof a network: physical proximity and social networks. To ourknowledge, we are the first to identify country-wide familiarstrangers utilizing both mobility and social networks. Weconfirm the existence of the phenomenon of a familiar strangerin an urban environment. At a macro scale, we found thatthe collective regularities - temporal regularity and spatialstructure - explain the phenomenon of familiar strangers.We also investigate the relationship between physical co-occurrences and the proximity in social networks and showthat physical co-occurrences indicate shorter social distancesvia a communication network. A series of landmark papershave established the regularity and predictability of humanmobility [11], [12]. Moreover, the understanding of collectiveregularity has implications for the prevention of epidemics andthe facilitation of information spreading.

We organize the paper as follows. We first describe thedata set and the settings we use to conduct our study. We testour hypothesis on the mechanism that drives the collectivebehavior of encountering. In the end, we overlay the physicalproximity network with phone communication network toexplore the relationships between them.

DATA AND SETTINGS

To capture both the social network and mobility network,we study the anonymized Call Detail Records of Andorra, aEuropean country, for July 2016. This dataset includes thecaller, receiver, connected cell tower, start and end time of theconnection. The spatial and social network encoded in Call De-tail Records enable us to identify familiar strangers. We createda communication network where each user is a vertex, and anedge exists if there exists direct contact between two users. InJuly, we are looking at a total of 1,264,292 users. After filteringout users with more than 100 connections that may be hotelsor vendors, we only consider the remaining 1,211,814 users.We identify the physical encounters by observing if two userscalled or text on the same tower within a one-hour windowof each other. In our study, we define familiar strangers asindividual pairs whom physical co-locate at one cell towerwithin the one-hour time window, but there exist no directlinks on the communication network.

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SPATIAL AND TEMPORAL PATTERNS OF ENCOUNTERS

To understand the temporal distribution of physical encoun-ters, we extract the time when an encounter happens as we seein Figure 2. There existed prominent spikes between workinghours (8 am - 11 am and 3 pm - 5 pm) on weekdays, andslight shifts for weekends (10 a.m. - 11 a.m. and 3 p.m. - 6p.m.). Interesting, we see a small peak at 11 p.m. on Saturdaynight, which captures the encounters of Saturday nightlife.

Fig. 1. Temporal distribution of physical encounters

We also analyze the spatial distribution of encounters,and the number of encounters happens for each encounterpair. More specifically, each tower has different usage that isdependent on the popularity around that tower, but there isalso a distribution over how many encounters happen betweentwo users at a single tower. As shown in Figure 2, there existssome towers that are not quite as popular with encounters, yetthey have some of the highest numbers of encounters countsbetween pairs of users.

Fig. 2. Map of cell towers, where the size of the node is proportional to totalnumber of encounters and the color is darker where a pair of users encountermore times on that tower.

COLLECTIVE REGULARITIES

Human mobility follows a high degree of temporal andspatial regularity [11], and physical encounter does not happenout of “coincidence”. We believe that collective regularityof human behaviors triggers the physical co-occurrences. Inparticular, we focus on the temporal regularities and spatialstructure of two consecutive encounters to uncover the under-lying mechanisms that drive the encounter.

A. Temporal regularity

Human daily routines, such as commuting, follow certaintemporal patterns. To explore the repeated encounters at apopulation scale, we create an encounter network based onmobility behaviors across a week and measure the inter-eventtime ∆t between consecutive encounters of each familiarstranger pair.

The left panel of Figure 3 shows the distribution of inter-event time between two encounters. We observe prominentpeaks for every 24 hours and another lower peaks for 24 ·d±6hour, where d is the dth day after the first encounter. Thispattern indicates that people are very likely to encounter theirfamiliar strangers on the same hour of a day within the next ddays. Also, we analyze the time of the consecutive encounters.We categorize the right panel of Figure 3 into two types ofencounters - weekday encounters and weekend encounters.Specifically, people who encounter during weekdays are lesslikely to encounter each other during weekends and vice versa.Besides, morning encounters are more likely to encounteragain during the morning, explaining the 24-hour peak asshown in the figure in the left panel. Both empirical exerciseshighlight the collective temporal regularity in people’s dailyroutines partly explains the repeated physical encounters.

Fig. 3. Temporal regularity of collective mobility behaviors. The left panelshows the probability density function of inter-event time (P∆t between twoconsecutive encounters. The right panel shows the encounter time of twoconsecutive co-locations

B. Spatial structure

We also investigate the spatial structure of repeated encoun-ters, specifically the popularity of the two locations, distancesbetween the two locations and the Points of Interests.

1) Popularity of and distances between the sequential en-counter locations: To gain insights on the encounter and re-encounter pairs, we use the general gravity model to under-stand the relationships between spatial distances, attractions(popularity) of the two locations. The gravity model utilized inour study assumes the following functional form, as shown in(1). We demonstrate the fit of the model and the relationshipsbetween encounter/ re-encounter flow and the variables ofinterests in Figure 4.

Tij = CNαi N

βj

Dγij

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where Tij is the number of encounter and re-encounterflow between two geographical location i and j. Dij is thedistance between two geographical areas and Ni and Nj arethe number of encounters of area i and j respectively. Afterapplying a logarithmic transformation and fit parameters witha linear regression, we found α = 0.38, β = 0.407, γ = 0.823.

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Fig. 4. Gravity law fit of encounter network. (A) Encounter and re-encounterflow obtained from data on the number of encounters the first and secondlocations, as a function of the distance between the encounter and re-encounterlocations. (B-D) Encounter and re-encounter flow as a function of distance,encounter popularity of first and second locations.

2) Points of Interests: The analysis of the Points of In-terests (POIs) surrounding cell towers enables us to infer trippurposes, the routines and the interests of the individual ([13],[14]). By analyzing the Points of Interests attached to thetwo consecutive locations, we have some intriguing empiricalfindings and need further investigation and generalization. Asshown in Figure 5, the warmer the color, the more likelyencounter and re-encounter happen at type A and type B POIs.As indicated by the color of each cell, the high probabilityencounter and re-encounter pair are food - food, the stadium- culture, culture - event and wellness - nature. The precedingpattern indicates that people who share the same interestsor within the same socio-demographic group are likely tomeet each other at another type of locations, which is in line

Fig. 5. Normalized transition probabilities from one to another type of POIs.X-axis is the POI type of the first encounter location and Y-axis is the POItype of the re-encounter location .

with Milgram’s finding in a small-scale experiment. Crandall(2010), has the similar observation on a large-scale data, inparticular, a minimal number of co-occurrences results in ahigh likelihood of a social tie, the negation of which mayinduce noises in masking acquaintances to be strangers [15].

FAMILIAR STRANGERS IN SOCIAL NETWORK

There exist studies establishing the relationships betweenmobility behaviors and social ties. Crandall (2010) developeda framework to empirically and mathematically investigate therelationship between social ties and co-occurrence [15]. Alongthe same line, Toole (2015) found that that the compositionof a user’s ego network concerning the type of contactsthey keep correlates with mobility behavior[16]. Apart fromthe observed relationship between mobility behavior and theprobability of the formation of a tie or the strength of a tie,we are specifically interested in the social distances between’strangers’ who physically encounter one another multiple dueto similar routines or interests. As shown in Figure 6, thereexists a negative relationship between social distance and thenumber of encounters - the more time each familiar strangerpair encounter one another, the closer they are on the socialnetworks. The spatial distributions of disconnected individualsand social distances in the social networks are shown in Figure7. We observe that the closer the encountering to the center ofthe country, the less likely two individuals will be disconnectedand closer they are on the social network.

C. Formation of community

As stated by Milgram, it is easier for familiar strangersto talk to each other if they meet in a different location. Inother words, collective behavior caused by similar inherentroutines may form an actual friendship due to a spatiotemporalcoincidence. In Figure 8, we show a time-resolved encounter-reencounter network. We can see that there exist communitiesconnected by nearby cell towers, such as Canillo, La Massana,and Encamp. However, the areas linked by warmer color areinteresting in that long-interval encounters to link them, which

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Fig. 6. Relationship between number of encounters and social distances insocial networks of familiar stranger pairs

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Fig. 7. Spatial distributions of disconnected individuals in social networkand social distances between two individuals in encounter pairs

indicates similar daily schedules. Pairs colored in purple notesimilar trajectory within 12 hours. Grey colors indicate peoplemay meet around 24 hours and Red red color indicate re-coincidence at around two days.

Fig. 8. Time-resolved encounter-reencounter network. Links with less than2000 encounter-reencounter pairs within a week is removed. The width is thelinks represents the counts of encounter-reencounter paris and the color of thelinks represents the time interval between encounter and reencounter.

DISCUSSIONS

The phenomenon of a familiar stranger has been formallyidentified by a small-scale experiment by Stanley Milgramsince 1972. However, there has been limited studies focusingon proving the phenomenon at a societal scale and inves-tigating the social relationships between familiar strangers.With the help of the large-scale mobile phone records, weempirically show the existence of the link in the country ofAndorra. Built upon the temporal and spatial distributions,we investigate the mechanisms that trigger this. In the end,we explore the relationship between social distances on thecommunication network and the number of encounters andshow that more substantial amount of encounters indicateshorter social distances on the social network.

In this study, we use the large-scale Call Detail Records ofa European country Andorra to create the physical encounternetwork and phone communication network. We show theexistence of the familiar stranger phenomenon in an urbanenvironment. By analyzing the temporal and spatial charac-teristics of the encounters, we uncover the underlying mech-anisms, especially collective temporal regularity and spatialstructure that trigger the phenomenon. In the end, we explorethe relationship between social distances along social networkand number of encounter in mobility network. We show that amore substantial amount of encounters predicts shorter socialdistances on social networks. The understanding of the physi-cal encounter network could have significant implications forepidemics preventions and information spreading facilitation.

Our study posits several interesting future studies. First ofall, one natural future work is to investigate how the rela-tionship of familiar strangers grows into an actual friendship,and how their behaviors intersect and synchronize with eachother. It would be even more interesting to understand thecausal relationships between physical co-occurrences and theformation of social ties. Another promising direction is to inte-

grate the familiar stranger relationships into the modeling andsimulation of epidemics spreading and information diffusion.

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