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Bo Söderberg¹

¹Complex Systems Division, Department of Theoretical Physics, Lund University, Sölvegatan 14A, S-22362 Lund, Sweden. Bo.Soderberg@thep.lu.se

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 26, 2003

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We introduce a new class of sparse random graph models using hidden edge-vertex coloring. This approach unifies existing models and allows for analytical calculation of graph properties, including component size distribution and percolation thresholds.

Area of Science:

Graph theory
Statistical physics
Network science

Background:

Existing random graph models often lack complex correlation structures.
A unified framework is needed to analyze diverse random graph ensembles.

Purpose of the Study:

To propose and investigate a unifying class of sparse random graph models.
To extend existing random graph approaches by incorporating hidden coloring.
To enable analytic calculation of graph characteristics.

Main Methods:

Utilizing a hidden coloring of edge-vertex incidences.
Extending random graphs with a given degree distribution.
Employing generating function techniques for analysis.

Main Results:

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The proposed model unifies several existing random graph ensembles.
The approach allows for the analytic calculation of observable graph characteristics.
Derived the size distribution of connected components and identified the percolation threshold.

Conclusions:

The unifying class of models provides a powerful framework for studying random graphs.
The method facilitates the analysis of correlation structures and emergent properties like giant components.