Abstract
Milgram empirically showed that people knowing only connections to their friends could locate any person in the U.S. in a few steps. Later research showed that social network topology enables a node aware of its full routing to find an arbitrary target in even fewer steps. Yet, the success of people in forwarding efficiently knowing only personal connections is still not fully explained. To study this problem, we emulate it on a real location-based social network, Gowalla. It provides explicit information about friends and temporal locations of each user useful for studies of human mobility. Here, we use it to conduct a massive computational experiment to establish new necessary and sufficient conditions for achieving social search efficiency. The results demonstrate that only the distribution of friendship edges and the partial knowledge of friends of friends are essential and sufficient for the efficiency of social search. Surprisingly, the efficiency of the search using the original distribution of friendship edges is not dependent on how the nodes are distributed into space. Moreover, the effect of using a limited knowledge that each node possesses about friends of its friends is strongly nonlinear. We show that gains of such use grow statistically significantly only when this knowledge is limited to a small fraction of friends of friends.
Highlights
Social search using Milgram rules has been extensively studied over the last 50 years
All collected data were anonymized according to the protocol approved by the RPI Institutional Review Board (IRB)
Since there are large differences between numbers of Gowalla users and populations in countries outside of the United States, here we analyze only data for users located in the U.S To ensure connectivity, we only consider the giant component of the analyzed network that comprises 75,803 users and 454,350 friendship edges, with the node Power Law degree exponent γ 1.49
Summary
Social search using Milgram rules has been extensively studied over the last 50 years. The problem involves tasking a person to utilize direct social connections to send a folder to a target person. The recipient should be a person who is most likely to increase the probability of the folder reaching the target. While there is a diverse body of work on this topic (see a thorough survey [1], the formulation used most frequently was defined in the initial Milgram’s small world experiments [2,3,4]). Milgram’s work was notable for being the first empirical social experiment in which individuals used only contacts with whom they were on a first-name basis. We will refer to a social search using the above rules as Milgram social
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