Heterogeneous network flow: a unifying framework characterising higher-order complex networks
File(s)
Author(s)
Ademovic Tahirovic, Alma
Type
Thesis
Abstract
Interacting subsystems are commonly described by networks. The notion of pairwise node interaction, however, typical of classic network analysis, is limiting. Recent research has demonstrated that most real-world systems expand beyond classic graph-based intuition, exhibiting higher-order complex network features. Interaction, furthermore, is often not dictated by topology alone, and may manifest as cross-layer information exchange, i.e., a form of multimodal network flow. Rationale can be found in most interacting subsystems, where a form of multimodal flow across layers can be observed in, e.g., chemical processes, energy networks, logistics, finance, or any other form of conversion process relying on conservation laws. To this end, the formal notion of heterogeneous network flow is proposed, a multilayer flow function aligned with the theory of network flow. The framework is defined with respect to an object that under invertible transformation conforms to a hypergraph, i.e., a Petri net. Petri net flow relations are further extended to incorporate both fundamental equations of balance, including cycle space constraints for domain specific applications. Dynamic equivalence is established with the Petri net framework, as baseline model for concurrent event systems. The proposed framework affords a number of theoretical and applied results, e.g., in machine learning, extended form of Laplacian flow, flow centrality, as well as graph learning-based inference of multilayer relationships over multimodal data, identifying multimodal interaction in real-world networked systems. Examples include, e.g.: the Petri Graph Neural Network, extending message passing graph neural networks to higher-order complex structures, improving expressive power, interpretability, and computational efficiency, demonstrating superior performance in, e.g., stock market price prediction; multimodal flow centrality, improving, e.g., critical component identification in IEEE test systems, and identifying inherent relative robustness of U.S. economic activity; or formal compliance with graph curvature and simplicial network geometry, offering additional formal conformities for future research, among other relevant application domains.
Version
Open Access
Date Issued
2023-12-05
Date Awarded
2024-03-01
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Strbac, Goran
Angeli, David
Publisher Department
Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)