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Anomaly detection in complex domains poses significant challenges due to the need for extensive labeled data and the inherently imbalanced nature of anomalous versus benign samples. Graph-based machine learning models have emerged as a promising solution that combines attribute and relational data to uncover intricate patterns. However, the scarcity of anomalous data exacerbates the challenge, which requires innovative strategies to enhance model learning with limited information. In this paper, we hypothesize that the incorporation of the influence of the nodes, quantified through average controllability, can significantly improve the performance of anomaly detection. We propose two novel approaches to integrate average controllability into graph-based frameworks: (1) using average controllability as an edge weight and (2) encoding it as a one-hot edge attribute vector. Through rigorous evaluation on real-world and synthetic networks with six state-of-the-art baselines, our proposed methods demonstrate improved performance in identifying anomalies, highlighting the critical role of controllability measures in enhancing the performance of graph machine learning models. This work underscores the potential of integrating average controllability as additional metrics to address the challenges of anomaly detection in sparse and imbalanced datasets. 

In this article, the author studies resilient strong structural controllability (SSC) in networks with misbehaving agents and edges. The author considers various misbehavior models and identifies the set of input agents offering resilience against such disruptions. The author's approach leverages a graph-based characterization of SSC, utilizing the concept of zero forcing in graphs. Specifically, the author examines three misbehavior models that disrupt the zero forcing process and compromise network SSC. The author then characterizes a leader set that guarantees SSC despite misbehaving nodes and edges, utilizing the concept of leaky forcing—a variation of zero forcing in graphs. The author's main finding reveals that resilience against one misbehavior model inherently provides resilience against others, thus simplifying the design process. Furthermore, the author explores combining multiple networks by augmenting edges between their nodes to achieve SSC in the combined network using a reduced leader set compared to the leader sets of individual networks. The author analyzes the tradeoff between added edges and leader set size in the resulting combined graph. Finally, the author discusses computational aspects and provides numerical evaluations to demonstrate the effectiveness of the author's approach. 

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.