# Complex networks with complex weights

arXiv: https://arxiv.org/abs/2212.06257 · HTML: https://mlsanity.com/paper/2212.06257/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2022.

## Built on by (most cited first, 9 of 9)

- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [Structural Balance and Random Walks on Complex Networks with Complex Weights](https://mlsanity.com/paper/2307.01813/) (2023)
- [Statistical Mechanics and Artificial Neural Networks: Principles, Models, and Applications](https://mlsanity.com/paper/2405.10957/) (2024)
- [Beyond symmetrization: effective adjacency matrices and renormalization for (un)singed directed graphs](https://mlsanity.com/paper/2406.01517/) (2024)
- [Matrix-weighted networks for modeling multidimensional dynamics](https://mlsanity.com/paper/2410.05188/) (2024)
- [Complex-Weighted Convolutional Networks: Provable Expressiveness via Complex Diffusion](https://mlsanity.com/paper/2511.13937/) (2025)
- [Graph energy as a measure of community detectability in networks](https://mlsanity.com/paper/2601.05065/) (2026)
- [Complex Diffusion Maps with ω-Parameterized Kernels Revealing Inherent Harmonic Representations](https://mlsanity.com/paper/2605.01691/) (2026)
- [Shortcomings and capacities of real-constrained neural networks in complex spaces](https://mlsanity.com/paper/2606.04390/) (2026)

## Abstract (arXiv)

In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to encode node--node interactions with heterogeneous intensities or frequencies (e.g., in transportation networks, supply chains, and social networks). Most such studies have considered real-valued weights, despite the fact that networks with complex weights arise in fields as diverse as quantum information, quantum chemistry, electrodynamics, rheology, and machine learning. Many of the standard network-science approaches in the study of classical systems rely on the real-valued nature of edge weights, so it is necessary to generalize them if one seeks to use them to analyze networks with complex edge weights. In this paper, we examine how standard network-analysis methods fail to capture structural features of networks with complex edge weights. We then generalize several network measures to the complex domain and show that random-walk centralities provide a useful approach to examine node importances in networks with complex weights.