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Optimal driver nodes in scale-free networks based on the spectral properties of the B matrix-sum of the Laplacian and the control matrices

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  • Ghoreishian Amiri, Fatemeh
  • Nazarimehr, Fahimeh
  • Jafari, Sajad
  • Towhidkhah, Farzad

Abstract

Controlling complex networks with minimal external input remains a fundamental challenge in network science. An efficient method is introduced for identifying optimal driver nodes in scale-free networks by maximizing the smallest eigenvalue of a specially constructed matrix B, defined as the sum of the Laplacian and control matrices. The proposed method is evaluated against six well-established approaches. The approach surpasses conventional heuristics in identifying high-impact control nodes. The findings offer new insights into the controllability of complex systems and identify promising directions for enhanced network-based interventions across various domains.

Suggested Citation

  • Ghoreishian Amiri, Fatemeh & Nazarimehr, Fahimeh & Jafari, Sajad & Towhidkhah, Farzad, 2026. "Optimal driver nodes in scale-free networks based on the spectral properties of the B matrix-sum of the Laplacian and the control matrices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 681(C).
    • Handle: RePEc:eee:phsmap:v:681:y:2026:i:c:s0378437125007162
    DOI: 10.1016/j.physa.2025.131064
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    References listed on IDEAS

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    1. Panahi, Shirin & Nazarimehr, Fahimeh & Jafari, Sajad & Sprott, Julien C. & Perc, Matjaž & Repnik, Robert, 2021. "Optimal synchronization of circulant and non-circulant oscillators," Applied Mathematics and Computation, Elsevier, vol. 394(C).
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