# A partial knowledge of friends of friends speeds social search

## TL;DR

This study investigates how partial knowledge of friends of friends in social networks influences search efficiency, revealing that limited, localized information significantly enhances social search performance without spatial distribution dependence.

## Contribution

The paper establishes new necessary and sufficient conditions for social search efficiency, emphasizing the role of friendship edge distribution and limited friends-of-friends knowledge.

## Key findings

- Partial knowledge of friends of friends improves search efficiency.
- Efficiency depends on friendship edge distribution, not spatial node distribution.
- Limited friends-of-friends knowledge yields nonlinear, significant gains.

## 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.