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Complexation Equilibria: Factors Influencing Stability of Complexes01:09

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In complexation reactions, metal cations are the electron pair acceptors, and the ligands are the electron pair donors. The stability of the metal complexes depends primarily on the complexing ability of the central metal ion and the nature of the ligands. Generally, the complexing ability of the metal ion depends on the size and charge of the ion. As the metal ion size increases, the stability of the metal complexes decreases, provided that the valency of the metal ion and the ligands remain...
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Updated: Feb 14, 2026

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Stability of a giant connected component in a complex network.

Maksim Kitsak1, Alexander A Ganin2,3, Daniel A Eisenberg3,4

  • 1Department of Physics, Northeastern University, 110 Forsyth Street, 111 Dana Research Center, Boston, Massachusetts 02115, USA.

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We studied network stability using link percolation. Robust single-layer networks are stable, but interdependent networks show instability, offering insights for resilient system design.

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Area of Science:

  • Network science
  • Complex systems analysis
  • Statistical physics

Background:

  • Understanding network resilience is crucial for critical infrastructure.
  • Adverse events can degrade network functionality.
  • Link percolation is a key model for network damage.

Purpose of the Study:

  • To analyze the stability of a network's giant connected component under adverse events.
  • To compare the stability of single-layered versus interdependent networks.
  • To provide insights for designing robust and resilient network topologies.

Main Methods:

  • Modeling adverse events using link percolation.
  • Quantifying the stability of the largest connected component.
  • Analyzing network robustness in single-layered and interdependent systems.

Main Results:

  • Single-layered networks with high-degree nodes exhibit robustness and stability.
  • Interdependent networks, despite robustness to failures, possess unstable connected components.
  • The stability of the giant connected component differs significantly between network types.

Conclusions:

  • Interdependent networks require different strategies for resilience compared to single-layered ones.
  • Findings inform the design of more stable and reliable networked systems.
  • This research contributes to enhancing the robustness of existing network infrastructures.