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Minimizing Spectral Radius of Non-Backtracking Matrix by Edge Removal

Published: 30 October 2021 Publication History

Abstract

The spectral radius of the non-backtracking matrix for an undirected graph plays an important role in various dynamic processes running on the graph. For example, its reciprocal provides an excellent approximation of epidemic and edge percolation thresholds. In this paper, we study the problem of minimizing the spectral radius of the non-backtracking matrix of a graph with n nodes and m edges, by deleting k selected edges. We show that the objective function of this combinatorial optimization problem is not submodular, although it is monotone. Since any straightforward approach to solving the optimization problem is computationally infeasible, we present an effective, scalable approximation algorithm with complexity O (n+km). Extensive experiment results for a large set of real-world networks verify the effectiveness and efficiency of our algorithm, and demonstrate that our algorithm outperforms several baseline schemes.

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cover image ACM Conferences
CIKM '21: Proceedings of the 30th ACM International Conference on Information & Knowledge Management
October 2021
4966 pages
ISBN:9781450384469
DOI:10.1145/3459637
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Published: 30 October 2021

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Author Tags

  1. centrality.
  2. edge removal
  3. epidemic threshold
  4. graph
  5. non-backtracking matrix
  6. spectral radius

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  • (2024)Finding the key nodes to minimize the victims of the malicious information in complex networkKnowledge-Based Systems10.1016/j.knosys.2024.111632293:COnline publication date: 7-Jun-2024
  • (2024)Controlling the spread of infectious diseases by using random walk method to remove many important linksCommunications in Nonlinear Science and Numerical Simulation10.1016/j.cnsns.2023.107658128(107658)Online publication date: Jan-2024
  • (2024)A control measure for epidemic spread based on the susceptible–infectious–susceptible (SIS) modelBioSystems10.1016/j.biosystems.2024.105341246(105341)Online publication date: Dec-2024
  • (2023)A Fast Algorithm for Moderating Critical Nodes via Edge RemovalIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2023.330998736:4(1385-1398)Online publication date: 30-Aug-2023
  • (2023)Measures and Optimization for Robustness and Vulnerability in Disconnected NetworksIEEE Transactions on Information Forensics and Security10.1109/TIFS.2023.327997918(3350-3362)Online publication date: 1-Jan-2023

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