Evaluating Stability in Massive Social Networks: Efficient Streaming Algorithms for Structural Balance

Authors Vikrant Ashvinkumar, Sepehr Assadi, Chengyuan Deng, Jie Gao , Chen Wang

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Vikrant Ashvinkumar
  • Department of Computer Science, Rutgers University, New Brunswick, NJ, USA
Sepehr Assadi
  • Department of Computer Science, Rutgers University, New Brunswick, NJ, USA
  • Cheriton School of Computer Science, University of Waterloo, Canada
Chengyuan Deng
  • Department of Computer Science, Rutgers University, New Brunswick, NJ, USA
Jie Gao
  • Department of Computer Science, Rutgers University, New Brunswick, NJ, USA
Chen Wang
  • Department of Computer Science, Rutgers University, New Brunswick, NJ, USA


We thank Karthik C.S. for some preliminary discussions.

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Vikrant Ashvinkumar, Sepehr Assadi, Chengyuan Deng, Jie Gao, and Chen Wang. Evaluating Stability in Massive Social Networks: Efficient Streaming Algorithms for Structural Balance. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 58:1-58:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Structural balance theory studies stability in networks. Given a n-vertex complete graph G = (V,E) whose edges are labeled positive or negative, the graph is considered balanced if every triangle either consists of three positive edges (three mutual "friends"), or one positive edge and two negative edges (two "friends" with a common "enemy"). From a computational perspective, structural balance turns out to be a special case of correlation clustering with the number of clusters at most two. The two main algorithmic problems of interest are: (i) detecting whether a given graph is balanced, or (ii) finding a partition that approximates the frustration index, i.e., the minimum number of edge flips that turn the graph balanced. We study these problems in the streaming model where edges are given one by one and focus on memory efficiency. We provide randomized single-pass algorithms for: (i) determining whether an input graph is balanced with O(log n) memory, and (ii) finding a partition that induces a (1 + ε)-approximation to the frustration index with O(n ⋅ polylog(n)) memory. We further provide several new lower bounds, complementing different aspects of our algorithms such as the need for randomization or approximation. To obtain our main results, we develop a method using pseudorandom generators (PRGs) to sample edges between independently-chosen vertices in graph streaming. Furthermore, our algorithm that approximates the frustration index improves the running time of the state-of-the-art correlation clustering with two clusters (Giotis-Guruswami algorithm [SODA 2006]) from n^O(1/ε²) to O(n²log³n/ε² + n log n ⋅ (1/ε)^O(1/ε⁴)) time for (1+ε)-approximation. These results may be of independent interest.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Theory of computation → Pseudorandomness and derandomization
  • Streaming algorithms
  • structural balance
  • pseudo-randomness generator


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