Graphicality of Power-Law Degree Sequences
Published:Dec 31, 2025 17:16
•1 min read
•ArXiv
Analysis
This paper investigates the graphicality problem (whether a degree sequence can form a simple graph) for power-law and double power-law degree sequences. It's important because understanding network structure is crucial in various applications. The paper provides insights into why certain sequences are not graphical, offering a deeper understanding of network formation and limitations.
Key Takeaways
- •Addresses the graphicality problem for power-law and double power-law degree sequences.
- •Combines sufficient and heuristic conditions to understand graphicality and non-graphicality.
- •Provides a phase diagram for double power-laws, identifying different ways graphicality can be violated.
- •Supports theoretical arguments with numerical analysis.
Reference
“The paper derives the graphicality of infinite sequences for double power-laws, uncovering a rich phase-diagram and pointing out the existence of five qualitatively distinct ways graphicality can be violated.”