Year: 2022
Type: article
Abstract: This paper presents a general recursive formula to estimate the number of labeled graphs as well as details to evaluate the formula for the following graph properties: number of edges (graph density), degree sequence, degree distribution, classification mixing, and degree mixing, i.e., the formula estimates the number of labeled graphs that have given values for graph properties. The proposed approach can be extended to additional graph properties (e.g., number of triangles) as well as properties of bipartite graphs. For special settings in which formulas exist from previous research, simulation studies demonstrate the validity of the proposed approach. In addition, we demonstrate how our approach can be used to quantify the level of variability in values of a graph property in the subset of graphs that hold a specified value of a different graph property (or properties) constant.
Source: Algorithms
DOI: 10.3390/a16010016
Authors: Ravi Goyal, Victor De Gruttola
Institutions: University of California San Diego, Harvard University
Language: English
Topic: Graph Theory and Algorithms
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,466
OpenAlex ID: W4312201401