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We study the parameterized complexity of the connected version of the vertex cover problem, where the solution set has to induce a connected subgraph. Although this problem does not admit a polynomial kernel for general graphs (unless NP is…
The complexity of highly interconnected systems is rooted in the interwoven architecture defined by its connectivity structure. In this paper, we develop matrix energy of the underlying connectivity structure as a measure of topological…
Convolutional Neural Networks (CNNs) are known for requiring extensive computational resources, and quantization is among the best and most common methods for compressing them. While aggressive quantization (i.e., less than 4-bits) performs…
Cortical thickness measurements from magnetic resonance imaging, an important biomarker in many neurodegenerative and neurological disorders, are derived by many tools from an initial voxel-wise tissue segmentation. White matter (WM)…
Cyclic structures are fundamental topological features in graphs, playing critical roles in network robustness, information flow, community structure, and various dynamic processes. Algorithmic tools that can efficiently probe and analyze…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…
In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the…
We study the distributed message-passing model in which a communication network is represented by a graph G=(V,E). Usually, the measure of complexity that is considered in this model is the worst-case complexity, which is the largest number…
Several important complex network measures that helped discovering common patterns across real-world networks ignore edge weights, an important information in real-world networks. We propose a new methodology for generalizing measures of…
Detecting and characterizing dense subgraphs (tight communities) in social and information networks is an important exploratory tool in social network analysis. Several approaches have been proposed that either (i) partition the whole…
High-throughput chromatin conformation capture (Hi-C) data provide insights into the 3D structure of chromosomes, with normalization being a crucial pre-processing step. A common technique for normalization is matrix balancing, which…
In this work, we study wavelet projection estimators for density estimation, focusing on their construction from $\mathcal{S}$-regular, compactly supported wavelet bases. A key aspect of such estimators is the choice of the resolution…
Although research on the control of networked systems has grown considerably, graph-theoretic and algorithmic studies on matrix-weighted graphs remain limited. To bridge this gap in the literature, this work introduces two algorithms-the…
Core-periphery (CP) structure is an important meso-scale network property where nodes group into a small, densely interconnected {core} and a sparse {periphery} whose members primarily connect to the core rather than to each other. While…
Vulnerability identification is crucial to protect the software systems from attacks for cyber security. It is especially important to localize the vulnerable functions among the source code to facilitate the fix. However, it is a…
This paper reexamines and fundamentally improves the Schmidl-and-Cox (S&C) algorithm, which is extensively used for packet detection in wireless networks, and enhances its adaptability for multi-antenna receivers. First, we introduce a new…
Weighted simplicial complexes (WSCs) are powerful tools for describing weighted cloud data or networks with weighted nodes. In this paper, we propose a novel approach to study WSCs via the concept of polarization. Polarization of a WSC…
This paper presents an exhaustive approach for verification of the weak reconstruction of Self Complementary Graphs up to 17 vertices. It describes the general problem of the Reconstruction Conjecture, explaining the complexity involved in…
The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first…