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This paper introduces a novel framework for graph sparsification that preserves the essential learning attributes of original graphs, improving computational efficiency and reducing complexity in learning algorithms. We refer to these sparse graphs as “learning backbones.” Our approach leverages the zero-forcing (ZF) phenomenon, a dynamic process on graphs with applications in network control. The key idea is to generate a tree from the original graph that retains critical dynamical properties. By correlating these properties with learning attributes, we construct effective learning backbones. We evaluate the performance of our ZF-based backbones in graph classification tasks across eight datasets and six baseline models. The results demonstrate that our method outperforms existing techniques. Additionally, we explore extensions using node distance metrics to further enhance the framework’s utility. 

This paper introduces a novel framework for graph sparsification that preserves the essential learning attributes of original graphs, improving computational efficiency and reducing complexity in learning algorithms. We refer to these sparse graphs as ``learning backbones.'' Our approach leverages the zero-forcing (ZF) phenomenon, a dynamic process on graphs with applications in network control. The key idea is to generate a tree from the original graph that retains critical dynamical properties. By correlating these properties with learning attributes, we construct effective learning backbones. We evaluate the performance of our ZF-based backbones in graph classification tasks across eight datasets and six baseline models. The results demonstrate that our method outperforms existing techniques. Additionally, we explore extensions using node distance metrics to further enhance the framework's utility. 

The graph distinguishability problem investigates whether a graph can be uniquely identified by the spectrum of its adjacency matrix, specifically determining if two graphs with the same spectrum are isomorphic. This issue is central to spectral graph theory and has significant implications for graph machine learning. In this paper, we explore the intricate connections between graph distinguishability and graph controllability–an essential concept in the control of networked systems. Focusing on oriented graphs and their skew-adjacency matrices, we establish controllability-based conditions that ensure their distinguishability. Notably, our conditions are less restrictive than existing methods, enabling a broader class of graphs to satisfy the distinguishability criteria. We illustrate the effectiveness of our results with several examples. Our findings highlight the applications of network control methods in tackling this crucial problem in algebraic graph theory, with implications for machine learning and network design. 

In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of ‘augmented’ graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph’s structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning. 

In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of ‘augmented’ graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph’s structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning. 

This paper studies the controllability backbone problem in dynamical networks defined over graphs. The main idea of the controllability backbone is to identify a small subset of edges in a given network such that any subnetwork containing those edges/links has at least the same network controllability as the original network while assuming the same set of input/leader vertices. We consider the strong structural controllability (SSC) in our work, which is useful but computationally challenging. Thus, we utilize two lower bounds on the network’s SSC based on the zero forcing notion and graph distances. We provide algorithms to compute controllability backbones while preserving these lower bounds. We thoroughly analyze the proposed algorithms and compute the number of edges in the controllability backbones. Finally, we compare and numerically evaluate our methods on random graphs.