Papers › Learning Networks from Random Walk-Based Node Similarities
Learning Networks from Random Walk-Based Node Similarities
Jeremy G. Hoskins, Cameron Musco, Christopher Musco, Charalampos E. Tsourakakis
Digital presence in the world of online social media entails significant privacy risks. In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such as effective resistances (i.e., commute times) or personalized PageRank scores. Using these similarities, the attacker's goal is to infer as much information as possible about the underlying network, including any remaining unknown pairwise node similarities and edges. For the effective resistance metric, we show that with just a small subset of measurements, the attacker can learn a large fraction of edges in a social network, even when the measurements are noisy. We also show that it is possible to learn a graph which accurately matches the underlying network on all other effective resistances. This second observation is interesting from a data mining perspective, since it can be expensive to accurately compute all effective resistances. As an alternative, our graphs learned from just a subset of approximate effective resistances can be used as surrogates in a wide range of applications that use effective resistances to probe graph structure, including for graph clustering, node centrality evaluation, and anomaly detection. We obtain our results by formalizing the graph learning objective mathematically, using two optimization problems. One formulation is convex and can be solved provably in polynomial time. The other is not, but we solve it efficiently with projected gradient and coordinate descent. We demonstrate the effectiveness of these methods on a number of social networks obtained from Facebook. We also discuss how our methods can be generalized to other random walk-based similarities, such as personalized PageRank. Our code is available at https://github.com/cnmusco/graph-similarity-learning.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections