PreprintCC BY 4.0arXiv
Generalized Discrete Fractal Dimensions of Graph Families
Abstract
Quantifying the self-similarity of complex networks via discrete fractal dimensions is a fundamental problem in network science. In this paper, we investigate some general fractal dimensions of graph families based on q-energy and Rényi entropy. We first establish several bounds for the energy, and then discuss the monotonicity, measure invariance of the dimensions, as well as some concrete graph families.
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BibTeX
@misc{liu2026generalized,
title = {{Generalized Discrete Fractal Dimensions of Graph Families}},
author = {Jiantao Liu and Cheng Zeng and Yumei Xue and Qingcheng Zeng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39187},
eprint = {2610.39187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39187},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generalized Discrete Fractal Dimensions of Graph Families
AU - Jiantao Liu
AU - Cheng Zeng
AU - Yumei Xue
AU - Qingcheng Zeng
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39187
UR - https://arxiv.org/abs/2610.39187
AB - Quantifying the self-similarity of complex networks via discrete fractal dimensions is a fundamental problem in network science. In this paper, we investigate some general fractal dimensions of graph families based on q-energy and Rényi entropy. We first establish several bounds for the energy, and then discuss the monotonicity, measure invariance of the dimensions, as well as some concrete graph families.
ER -