Reducible Iterated Graph Systems: multiscale-freeness and multifractals

Journal article

Iterated graph systems (IGS) transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous definitions of multifractality and multiscale-freeness for fractal graphs, and we establish conditions that are equivalent to the occurrence of these two phenomena. We further determine the corresponding fractal and degree spectra, proving that both are finite and discrete. These results complete the foundational theory of Edge IGS by filling the gap left by the primitive case studied in Li et al and Neroli (2024 Proc. Am. Math. Soc. 152 1377–89; 2024 Proc. R. Soc. A 480 20240406)

Authors: Li, NZ; Hu, FX; Britz, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Nonlinearity
• Volume: 39
• Issue: 4
• Pages: 045009
• Article number: 045009
• Publication date: 2026-04-10
• Acceptance date: 2026-03-30
• DOI: 10.1088/1361-6544/ae58e5
• EISSN: 1361-6544
• ISSN: 0951-7715
• Language: English
• Keywords: Iterated Graph Systems; 28A80; multifractal; multiscale-free; 05C82