A Jacobi diffusion on graphon space is discretized into a graph-level generative process that matches the continuous process's first moment exactly and second moment up to a closed-form gap, enabling out-of-scale graph generation.
Graphons of Line Graphs
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We consider the problem of estimating graph limits, known as graphons, from observations of sequences of sparse finite graphs. In this paper we show a simple method that can shed light on a subset of sparse graphs. The method involves mapping the original graphs to their line graphs. We show that graphs satisfying a particular property, which we call the square-degree property are sparse, but give rise to dense line graphs. This enables the use of results on graph limits of dense graphs to derive convergence. In particular, star graphs satisfy the square-degree property resulting in dense line graphs and non-zero graphons of line graphs. We demonstrate empirically that we can distinguish different numbers of stars (which are sparse) by the graphons of their corresponding line graphs. Whereas in the original graphs, the different number of stars all converge to the zero graphon due to sparsity. Similarly, superlinear preferential attachment graphs give rise to dense line graphs almost surely. In contrast, dense graphs, including Erdos-Renyi graphs make the line graphs sparse, resulting in the zero graphon.
fields
stat.ML 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
DiPhon: Diffusion on Graphons for Scalable Graph Generation
A Jacobi diffusion on graphon space is discretized into a graph-level generative process that matches the continuous process's first moment exactly and second moment up to a closed-form gap, enabling out-of-scale graph generation.