Low-distortion inference of latent similarities from a multiplex social network

Ittai Abraham, Shiri Chechik, David Kempe, Aleksandrs Slivkins

Research output: Contribution to journalArticlepeer-review


Much of social network analysis is-implicitly or explicitly-predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the latent underlying "social space"-the way in which individuals are similar or dissimilar. Many research questions frequently addressed via social network analysis are in reality questions about this social space, raising the question of inverting the process: Given a social network, how accurately can we reconstruct the social structure of similarities and dissimilarities? We begin to address this problem formally. Observed social networks are usually multiplex, in the sense that they reflect (dis)similarities in several different "categories," such as geographical proximity, kinship, or similarity of professions/hobbies. We assume that each such category is characterized by a latent metric capturing (dis)similarities in this category. Each category gives rise to a separate social network: a random graph parameterized by this metric. For a concrete model, we consider Kleinberg's small world model and some variations thereof. The observed social network is the unlabeled union of these graphs; i.e., the presence or absence of edges can be observed, but not their origins. Our main result is an efficient algorithm which reconstructs each metric with provably low distortion.

Original languageEnglish
Pages (from-to)617-668
Number of pages52
JournalSIAM Journal on Computing
Issue number3
StatePublished - 2015


FundersFunder number
Microsoft Research
Weizmann Institute of Science


    • Metric space
    • Multiplex social networks
    • Small world networks
    • Social distance
    • Social network analysis


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