arXiv subjects

Waseem Abbas

Publications and source records attributed to Waseem Abbas.

At least 19 recordsLinked to original sources

arXiv2026

On the number of generalized cospectral mates of graphs

This paper establishes an upper bound on the number of generalized cospectral mates of simple graphs, where the generalized spectrum consists of the spectrum of a graph and its complement. Moving beyond the classical problem of identifying graphs determined by their generalized spectrum, we address the more quantitative question of how many non-isomorphic graphs can share the same generalized spectrum. Our approach is based on arithmetic constraints derived from the Smith Normal Form (SNF) of the walk matrix, which leads to a tight upper bound on the number of generalized cospectral mates of a graph. Our upper bound applies to a much broader class of graphs than those previously shown to have no generalized cospectral mates (graphs determined by generalized spectrum). Consequently, this work extends the family of graphs for which strong and informative spectral uniqueness results are available

math.CO↗

arXiv2025

Quantifying the Generalization Gap: A New Benchmark for Out-of-Distribution Graph-Based Android Malware Classification

While graph-based Android malware classifiers achieve over 94% accuracy on standard benchmarks, they exhibit a significant generalization gap under distribution shift, suffering up to 45% performance degradation when encountering unseen malware variants from known families. This work systematically investigates this critical yet overlooked challenge for real-world deployment by introducing a benchmarking suite designed to simulate two prevalent scenarios: MalNet-Tiny-Common for covariate shift, and MalNet-Tiny-Distinct for domain shift. Furthermore, we identify an inherent limitation in existing benchmarks where the inputs are structure-only function call graphs, which fails to capture the latent semantic patterns necessary for robust generalization. To verify this, we construct a semantic enrichment framework that augments the original topology with function-level attributes, including lightweight metadata and LLM-based code embeddings. By providing this expanded feature set, we aim to equip future research with richer behavioral information to facilitate the development of more sophisticated detection techniques. Empirical evaluations confirm the effectiveness of our data-centric methodology, with which classification performs better under distribution shift compared to model-based approaches, and consistently further enhances robustness when used in conjunction. We release our precomputed datasets, along with an extensible implementation of our comprehensive pipeline, to lay the groundwork for building resilient malware detection systems for evolving threat environments.

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arXiv2025

Feature Construction Using Network Control Theory and Rank Encoding for Graph Machine Learning

In this article, we utilize the concept of average controllability in graphs, along with a novel rank encoding method, to enhance the performance of Graph Neural Networks (GNNs) in social network classification tasks. GNNs have proven highly effective in various network-based learning applications and require some form of node features to function. However, their performance is heavily influenced by the expressiveness of these features. In social networks, node features are often unavailable due to privacy constraints or the absence of inherent attributes, making it challenging for GNNs to achieve optimal performance. To address this limitation, we propose two strategies for constructing expressive node features. First, we introduce average controllability along with other centrality metrics (denoted as NCT-EFA) as node-level metrics that capture critical aspects of network topology. Building on this, we develop a rank encoding method that transforms average controllability or any other graph-theoretic metric into a fixed-dimensional feature space, thereby improving feature representation. We conduct extensive numerical evaluations using six benchmark GNN models across four social network datasets to compare different node feature construction methods. Our results demonstrate that incorporating average controllability into the feature space significantly improves GNN performance. Moreover, the proposed rank encoding method outperforms traditional one-hot degree encoding, improving the ROC AUC from 68.7% to 73.9% using GraphSAGE on the GitHub Stargazers dataset, underscoring its effectiveness in generating expressive and efficient node representations.

cs.LG↗

arXiv2025

Robust Anomaly Detection with Graph Neural Networks using Controllability

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.

cs.LG↗

arXiv2025

Walk Matrix-Based Upper Bounds on Generalized Cospectral Mates

The problem of characterizing graphs determined by their spectrum (DS) or generalized spectrum (DGS) has been a longstanding topic of interest in spectral graph theory, originating from questions in chemistry and mathematical physics. While previous studies primarily focus on identifying whether a graph is DGS, we address a related yet distinct question: how many non-isomorphic generalized cospectral mates a graph can have? Building upon recent advances that connect this question to the properties of the walk matrix, we introduce a broad family of graphs and establish an explicit upper bound on the number of non-isomorphic generalized cospectral mates they can have. This bound is determined by the arithmetic structure of the determinant of the walk matrix, offering a refined criterion for quantifying the multiplicity of generalized cospectral graphs. This result sheds new light on the structure of generalized cospectral graphs and provides a refined arithmetic criterion for bounding their multiplicity.

math.CO↗

arXiv2025

An upper bound on generalized cospectral mates of oriented hraphs using skew-walk matrices

Let $D$ be an oriented graph with skew-adjacency matrix $S(D)$. Two oriented graphs $D$ and $C$ are said to share the same generalized skew spectrum if $S(D)$ and $S(C)$ have the same eigenvalues, and $J-S(D)$ and $J-S(C)$ also have the same eigenvalues, where $J$ is the all-ones matrix. Such graphs that are not isomorphic are generalized cospectral mates. We derive tight upper bounds on the number of generalized cospectral mates that an oriented graph can admit, based on arithmetic criteria involving the determinant of its skew-walk matrix. As a special case, we also provide a criterion for an oriented graph to be weakly determined by its generalized skew spectrum (WDGSS), that is, its only generalized cospectral mate is its transpose. These criteria relate directly to the controllability of graphs, a fundamental concept in the control of networked systems, thereby connecting spectral characterization of graphs to graph controllability.

math.CO↗

arXiv2025

Learning Backbones: Sparsifying Graphs through Zero Forcing for Effective Graph-Based Learning

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.

cs.LG↗

arXiv2024

PropEnc: A Property Encoder for Graph Neural Networks

Graph machine learning, particularly using graph neural networks, heavily relies on node features. However, many real-world systems, such as social and biological networks, lack node features due to privacy concerns, incomplete data, or collection limitations. Structural and positional encoding are commonly used to address this but are constrained by the maximum values of the encoded properties, such as the highest node degree. This limitation makes them impractical for scale-free networks and applications involving large or non-categorical properties. This paper introduces PropEnc, a novel and versatile encoder to generate expressive node embedding from any graph metric. By combining histogram construction with reversed index encoding, PropEnc offers a flexible solution that supports low-dimensional representations and diverse input types, effectively mitigating sparsity issues while improving computational efficiency. Additionally, it replicates one-hot encoding or approximates indices with high accuracy, making it adaptable to a wide range of graph applications. We validate PropEnc through extensive experiments on graph classification task across several social networks lacking node features. The empirical results demonstrate that PropEnc offers an efficient mechanism for constructing node features from various graph metrics.

cs.LG↗

arXiv2024

Improving Graph Machine Learning Performance Through Feature Augmentation Based on Network Control Theory

Network control theory (NCT) offers a robust analytical framework for understanding the influence of network topology on dynamic behaviors, enabling researchers to decipher how certain patterns of external control measures can steer system dynamics towards desired states. Distinguished from other structure-function methodologies, NCT's predictive capabilities can be coupled with deploying Graph Neural Networks (GNNs), which have demonstrated exceptional utility in various network-based learning tasks. However, the performance of GNNs heavily relies on the expressiveness of node features, and the lack of node features can greatly degrade their performance. Furthermore, many real-world systems may lack node-level information, posing a challenge for GNNs.To tackle this challenge, we introduce a novel approach, NCT-based Enhanced Feature Augmentation (NCT-EFA), that assimilates average controllability, along with other centrality indices, into the feature augmentation pipeline to enhance GNNs performance. Our evaluation of NCT-EFA, on six benchmark GNN models across two experimental setting. solely employing average controllability and in combination with additional centrality metrics. showcases an improved performance reaching as high as 11%. Our results demonstrate that incorporating NCT into feature enrichment can substantively extend the applicability and heighten the performance of GNNs in scenarios where node-level information is unavailable.

cs.LG↗

arXiv2024

Control-based Graph Embeddings with Data Augmentation for Contrastive 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.

cs.LG↗

arXiv2024

A Geometric Approach to Resilient Distributed Consensus Accounting for State Imprecision and Adversarial Agents

This paper presents a novel approach for resilient distributed consensus in multiagent networks when dealing with adversarial agents imprecision in states observed by normal agents. Traditional resilient distributed consensus algorithms often presume that agents have exact knowledge of their neighbors' states, which is unrealistic in practical scenarios. We show that such existing methods are inadequate when agents only have access to imprecise states of their neighbors. To overcome this challenge, we adapt a geometric approach and model an agent's state by an `imprecision region' rather than a point in $\mathbb{R}^d$. From a given set of imprecision regions, we first present an efficient way to compute a region that is guaranteed to lie in the convex hull of true, albeit unknown, states of agents. We call this region the \emph{invariant hull} of imprecision regions and provide its geometric characterization. Next, we use these invariant hulls to identify a \emph{safe point} for each normal agent. The safe point of an agent lies within the convex hull of its \emph{normal} neighbors' states and hence is used by the agent to update it's state. This leads to the aggregation of normal agents' states to safe points inside the convex hull of their initial states, or an approximation of consensus. We also illustrate our results through simulations. Our contributions enhance the robustness of resilient distributed consensus algorithms by accommodating state imprecision without compromising resilience against adversarial agents.

eess.SY↗

arXiv2023

Enhanced Graph Neural Networks with Ego-Centric Spectral Subgraph Embeddings Augmentation

Graph Neural Networks (GNNs) have shown remarkable merit in performing various learning-based tasks in complex networks. The superior performance of GNNs often correlates with the availability and quality of node-level features in the input networks. However, for many network applications, such node-level information may be missing or unreliable, thereby limiting the applicability and efficacy of GNNs. To address this limitation, we present a novel approach denoted as Ego-centric Spectral subGraph Embedding Augmentation (ESGEA), which aims to enhance and design node features, particularly in scenarios where information is lacking. Our method leverages the topological structure of the local subgraph to create topology-aware node features. The subgraph features are generated using an efficient spectral graph embedding technique, and they serve as node features that capture the local topological organization of the network. The explicit node features, if present, are then enhanced with the subgraph embeddings in order to improve the overall performance. ESGEA is compatible with any GNN-based architecture and is effective even in the absence of node features. We evaluate the proposed method in a social network graph classification task where node attributes are unavailable, as well as in a node classification task where node features are corrupted or even absent. The evaluation results on seven datasets and eight baseline models indicate up to a 10% improvement in AUC and a 7% improvement in accuracy for graph and node classification tasks, respectively.

cs.SI↗

arXiv2023

Controllability Backbone in Networks

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.

eess.SY↗

arXiv2023

A Survey of Graph Unlearning

Graph unlearning emerges as a crucial advancement in the pursuit of responsible AI, providing the means to remove sensitive data traces from trained models, thereby upholding the \textit{right to be forgotten}. It is evident that graph machine learning exhibits sensitivity to data privacy and adversarial attacks, necessitating the application of graph unlearning techniques to address these concerns effectively. In this comprehensive survey paper, we present the first systematic review of graph unlearning approaches, encompassing a diverse array of methodologies and offering a detailed taxonomy and up-to-date literature overview to facilitate the understanding of researchers new to this field. To ensure clarity, we provide lucid explanations of the fundamental concepts and evaluation measures used in graph unlearning, catering to a broader audience with varying levels of expertise. Delving into potential applications, we explore the versatility of graph unlearning across various domains, including but not limited to social networks, adversarial settings, recommender systems, and resource-constrained environments like the Internet of Things, illustrating its potential impact in safeguarding data privacy and enhancing AI systems' robustness. Finally, we shed light on promising research directions, encouraging further progress and innovation within the domain of graph unlearning. By laying a solid foundation and fostering continued progress, this survey seeks to inspire researchers to further advance the field of graph unlearning, thereby instilling confidence in the ethical growth of AI systems and reinforcing the responsible application of machine learning techniques in various domains.

cs.LG↗

arXiv2023

Computing Graph Descriptors on Edge Streams

Feature extraction is an essential task in graph analytics. These feature vectors, called graph descriptors, are used in downstream vector-space-based graph analysis models. This idea has proved fruitful in the past, with spectral-based graph descriptors providing state-of-the-art classification accuracy. However, known algorithms to compute meaningful descriptors do not scale to large graphs since: (1) they require storing the entire graph in memory, and (2) the end-user has no control over the algorithm's runtime. In this paper, we present streaming algorithms to approximately compute three different graph descriptors capturing the essential structure of graphs. Operating on edge streams allows us to avoid storing the entire graph in memory, and controlling the sample size enables us to keep the runtime of our algorithms within desired bounds. We demonstrate the efficacy of the proposed descriptors by analyzing the approximation error and classification accuracy. Our scalable algorithms compute descriptors of graphs with millions of edges within minutes. Moreover, these descriptors yield predictive accuracy comparable to the state-of-the-art methods but can be computed using only 25% as much memory.

cs.LG↗

arXiv2023

Distributed Design of Controllable and Robust Networks using Zero Forcing and Graph Grammars

This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes $N$, the number of leaders $N_L$, and diameter $D$, where $2 \le D \le N/N_L$, we propose graph constructions generating strong structurally controllable networks. We also compute the number of edges in graphs, which are maximal for improved robustness measured by the algebraic connectivity and Kirchhoff index. For the controllability analysis, we utilize the notion of zero forcing sets in graphs. Additionally, we present graph grammars, which are sets of rules that agents apply in a distributed manner to construct the graphs mentioned above. We also numerically evaluate our methods. This work exploits the trade-off between network controllability and robustness and generates networks satisfying multiple design criteria.

eess.SY↗

arXiv2023

Resilient Strong Structural Controllability in Networks using Leaky Forcing in Graphs

This paper studies the problem of selecting input nodes (leaders) to make networks strong structurally controllable despite misbehaving nodes and edges. We utilize a graph-based characterization of network strong structural controllability (SSC) in terms of zero forcing in graphs, which is a dynamic coloring of nodes. We consider three types of misbehaving nodes and edges that disrupt the zero forcing process in graphs, thus, deteriorating the network SSC. Then, we examine a leader selection guaranteeing network SSC by ensuring the accuracy of the zero forcing process, despite $k$ misbehaving nodes/edges. Our main result shows that a network is resilient to $k$ misbehaving nodes/edges under one threat model if and only if it is resilient to the same number of failures under the other threat models. Thus, resilience against one threat model implies resilience against the other models. We then discuss the computational aspects of leader selection for resilient SSC and present a numerical evaluation.

eess.SY↗

arXiv2021

Resilient Distributed Vector Consensus Using Centerpoints

In this paper, we study the resilient vector consensus problem in networks with adversarial agents and improve resilience guarantees of existing algorithms. A common approach to achieving resilient vector consensus is that every non-adversarial (or normal) agent in the network updates its state by moving towards a point in the convex hull of its \emph{normal} neighbors' states. Since an agent cannot distinguish between its normal and adversarial neighbors, computing such a point, often called as \emph{safe point}, is a challenging task. To compute a safe point, we propose to use the notion of \emph{centerpoint}, which is an extension of the median in higher dimensions, instead of Tverberg partition of points, which is often used for this purpose. We discuss that the notion of centerpoint provides a complete characterization of safe points in $\mathbb{R}^d$. In particular, we show that a safe point is essentially an interior centerpoint if the number of adversaries in the neighborhood of a normal agent $i$ is less than $\frac{N_i}{d+1} $, where $d$ is the dimension of the state vector and $N_i$ is the total number of agents in the neighborhood of $i$. Consequently, we obtain necessary and sufficient conditions on the number of adversarial agents to guarantee resilient vector consensus. Further, by considering the complexity of computing centerpoints, we discuss improvements in the resilience guarantees of vector consensus algorithms and compare with the other existing approaches. Finally, we numerically evaluate the performance of our approach through experiments.

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