An efficient reconciliation algorithm for social networks (1307.1690v2)

Abstract: People today typically use multiple online social networks (Facebook, Twitter, Google+, LinkedIn, etc.). Each online network represents a subset of their "real" ego-networks. An interesting and challenging problem is to reconcile these online networks, that is, to identify all the accounts belonging to the same individual. Besides providing a richer understanding of social dynamics, the problem has a number of practical applications. At first sight, this problem appears algorithmically challenging. Fortunately, a small fraction of individuals explicitly link their accounts across multiple networks; our work leverages these connections to identify a very large fraction of the network. Our main contributions are to mathematically formalize the problem for the first time, and to design a simple, local, and efficient parallel algorithm to solve it. We are able to prove strong theoretical guarantees on the algorithm's performance on well-established network models (Random Graphs, Preferential Attachment). We also experimentally confirm the effectiveness of the algorithm on synthetic and real social network data sets.

• The paper introduces a mathematically formalized reconciliation problem and proposes a novel algorithm with provable performance guarantees.
• It utilizes user-provided seed links and neighborhood similarity scores to iteratively match high-degree nodes and then lower-degree nodes.
• Empirical results on synthetic and real-world datasets demonstrate high precision, recall, scalability, and robustness against malicious interference.

Overview of "An Efficient Reconciliation Algorithm for Social Networks"

In the paper "An Efficient Reconciliation Algorithm for Social Networks", authors Nitish Korula and Silvio Lattanzi address the challenge of reconciling online social networks by identifying all accounts that belong to the same individual across various platforms. This problem is both practically and theoretically significant, as it can enhance our understanding of social dynamics and improve applications such as personalized content delivery.

Problem Formalization and Contributions

The paper's primary contributions include a formal mathematical definition of the social network reconciliation problem and the development of a novel algorithm with provable theoretical performance guarantees. Notably, the paper leverages initial links created by users themselves across networks as a foundational data set to bootstrap the reconciliation process.

Models and Assumptions

To tackle the reconciliation problem, the authors model the underlying “true” social network and consider it as being partitioned into multiple online representations, such as Facebook, Twitter, etc. These representations are conceptualized using well-established models like Random Graphs and Preferential Attachment. The two main assumptions are:

1. Edge Survival: Connections in the true social network appear in each online representation with some probability.
2. Initial Seed Links: A fraction of users already have their connections across networks publicly linked.

Algorithm Design

The algorithm proposed is efficient, local, parallelizable, and robust against malicious users. It iteratively identifies and links user accounts across networks by optimizing for similarity in network neighborhoods.

1. Similarity Witnesses: The core idea involves computing a similarity score for pairs of nodes across networks by counting shared neighbors who have been identified in previous iterations.
2. Degree-Based Initialization: Initially high-degree nodes serve as the foundational identification layer, progressively leading to the identification of lower-degree nodes.

Theoretical Guarantees

The authors provide rigorous proofs of their algorithm's efficacy, particularly for random graph models and preferential attachment graphs. They establish that despite similarities to the graph isomorphism problem, the reconciliation task benefits from real-world network structures and initial seed links, overcoming theoretical intractability.

Experimental Validation

Empirical results bolster the theoretical claims with experiments on synthetic graphs generated by models like Preferential Attachment and real-world networks such as Facebook, DBLP, and Wikipedia.

1. Precision and Recall: High precision (low error rates) and substantial recall (the proportion of correctly identified links) characterize the algorithm's performance across various datasets.
2. Scalability and Robustness: The algorithm scales efficiently to large network sizes and withstands variations in model assumptions and attack scenarios, such as the presence of malicious entities trying to confuse the reconciliation process.

Implications and Future Directions

This research has profound implications for the paper and utility of social networks. By providing a method to link user interactions across diverse platforms, it can lead to more comprehensive analytics and personalized services. The algorithm's robustness and efficiency make it suitable for real-time applications in dynamic environments.

Future research could extend these findings to newer models of social networks, investigate alternative initial link strategies, and apply the algorithm to even more heterogeneous and cross-domain databases beyond social networks. This can further refine our understanding of individual presence in digital spheres and contribute to privacy-preserving strategies in network analysis.