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Updated: Apr 16, 2026
06:55
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
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Exactly solvable model of a coalescing random graph
1Geophysical Center of Russian Academy of Science, 3, Molodezhnaya Street, 119296 Moscow, Russia and National Research Nuclear University MEPhI, 31, Kashirskoye Road, 115409 Moscow, Russia.
Summary
This study models graph evolution, revealing a phase transition where a giant component emerges. The research analyzes the kinetics of this giant component
Area of Science:
- Graph theory
- Statistical physics
- Network science
Background:
- Graphs evolve by edge addition, forming components.
- Finite vertex valence limits graph structure.
- Understanding component dynamics is crucial.
Purpose of the Study:
- Formulate and solve the kinetic equation for graph component distribution.
- Analyze the emergence and growth of a giant component.
- Determine time dependencies of giant component properties.
Main Methods:
- Random edge addition model.
- Kinetic equation formulation.
- Generating function method for solving equations.
Main Results:
- A phase transition leads to a giant component.
- Kinetics of giant component growth identified.
- Time-dependent average order and valence derived.
Conclusions:
- Graph evolution exhibits a critical phase transition.
- The giant component's growth is characterized.
- Component distribution is determined for initial conditions.
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