TY - JOUR

T1 - The gravitational law of social interaction

AU - Levy, Moshe

AU - Goldenberg, Jacob

PY - 2014/1/1

Y1 - 2014/1/1

N2 - While a great deal is known about the topology of social networks, there is much less agreement about the geographical structure of these networks. The fundamental question in this context is: how does the probability of a social link between two individuals depend on the physical distance between them? While it is clear that the probability decreases with the distance, various studies have found different functional forms for this dependence. The exact form of the distance dependence has crucial implications for network searchability and dynamics: Kleinberg (2000) [15] shows that the small-world property holds if the probability of a social link is a power-law function of the distance with power -2, but not with any other power. We investigate the distance dependence of link probability empirically by analyzing four very different sets of data: Facebook links, data from the electronic version of the Small-World experiment, email messages, and data from detailed personal interviews. All four datasets reveal the same empirical regularity: the probability of a social link is proportional to the inverse of the square of the distance between the two individuals, analogously to the distance dependence of the gravitational force. Thus, it seems that social networks spontaneously converge to the exact unique distance dependence that ensures the Small-World property.

AB - While a great deal is known about the topology of social networks, there is much less agreement about the geographical structure of these networks. The fundamental question in this context is: how does the probability of a social link between two individuals depend on the physical distance between them? While it is clear that the probability decreases with the distance, various studies have found different functional forms for this dependence. The exact form of the distance dependence has crucial implications for network searchability and dynamics: Kleinberg (2000) [15] shows that the small-world property holds if the probability of a social link is a power-law function of the distance with power -2, but not with any other power. We investigate the distance dependence of link probability empirically by analyzing four very different sets of data: Facebook links, data from the electronic version of the Small-World experiment, email messages, and data from detailed personal interviews. All four datasets reveal the same empirical regularity: the probability of a social link is proportional to the inverse of the square of the distance between the two individuals, analogously to the distance dependence of the gravitational force. Thus, it seems that social networks spontaneously converge to the exact unique distance dependence that ensures the Small-World property.

KW - Distance dependence

KW - Gravitational law

KW - Link probability

KW - Searchability

KW - Small world

KW - Social networks

UR - http://www.scopus.com/inward/record.url?scp=84886597174&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2013.08.067

DO - 10.1016/j.physa.2013.08.067

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AN - SCOPUS:84886597174

SN - 0378-4371

VL - 393

SP - 418

EP - 426

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -