Are Erd\"os- R\'enyi Random Graphs Topologically Random?
Keith Smith, Javier Escudero
TL;DR
This paper demonstrates that Erdős-Rényi random graphs do not exhibit topological randomness, challenging assumptions about their structural properties.
Contribution
It provides a formal proof that Erdős-Rényi graphs are not topologically random, clarifying their structural limitations.
Findings
Erdős-Rényi graphs lack topological randomness
Theoretical proof of non-random topological structure
Challenges previous assumptions about graph randomness
Abstract
No. We prove that Erdos- Renyi Random Graphs are not topologically random.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Mathematical Dynamics and Fractals · Computability, Logic, AI Algorithms