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Infinite Ergodic Walks in Finite Connected Undirected Graphs
1Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA.
Entropy (Basel, Switzerland)
|February 11, 2021
Summary
We introduce entropic force and pressure to quantify graph defects and their impact on long walks. This helps analyze network structure, mobility, and navigability in finite graphs.
Area of Science:
- Statistical Mechanics
- Network Science
- Graph Theory
Background:
- Ensembles of walks (micro-canonical, canonical, grand canonical) are studied in finite graphs.
- Infinite walk length highlights sensitivity to structural irregularities and defects.
Purpose of the Study:
- To describe structural imbalance, anisotropy, and navigability in finite graphs using properties of infinitely long walks.
- To introduce novel concepts of entropic force and pressure to quantify the impact of graph defects.
Main Methods:
- Analysis of walk ensembles in the thermodynamic limit (infinite walk length).
- Development of entropic force and pressure metrics to characterize graph defects.
Main Results:
- Infinitely long walks reveal graph structural properties like imbalance and anisotropy.
- New entropic force and pressure concepts quantify defect effects on mobility and navigation.
- Node fugacity is introduced for analyzing network dynamics during expansion or shrinking.
Conclusions:
- The study provides new tools to analyze complex network structures and dynamics.
- Entropic force and pressure offer insights into graph navigability and defect impact.
- Findings are applicable to understanding and predicting network behavior.
Keywords:
entropic force and pressuregraph node’s fugacitygraph node’s navigabilitygraph’s navigationstatistical ensembles of walksMore Related Videos
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