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Industrial components are of high importance because they control critical infrastructures that form the lifeline of modern societies. However, the rapid evolution of industrial components, together with the new paradigm of Industry 4.0,…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
This paper proposes a novel branch-and-bound(BMWVC) algorithm to exactly solve the minimum weight vertex cover problem (MWVC) in large graphs. The original contribution is several new graph reduction rules, allowing to reduce a graph G and…
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 $D$,…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Given a data graph G, a source vertex u and a target vertex v of a reachability query, the reachability query is used to answer whether there exists a path from u to v in G. Reachability query processing is one of the fundamental operations…
The mathematical analysis of robustness and error-tolerance of complex networks has been in the center of research interest. On the other hand, little work has been done when the attack-tolerance of the vertices or edges are not independent…
Cyberattacks on enterprise networks exploit complex dependencies among infrastructure, services, and applications, which challenge traditional analysis methods that focus on attack paths or network topology in isolation. In this study, we…
Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…
Graph classification is a pivotal challenge in machine learning, especially within the realm of graph-based data, given its importance in numerous real-world applications such as social network analysis, recommendation systems, and…
The $k$-core decomposition is a widely studied summary statistic that describes a graph's global connectivity structure. In this paper, we move beyond using $k$-core decomposition as a tool to summarize a graph and propose using $k$-core…
The theory of kernelization can be used to rigorously analyze data reduction for graph coloring problems. Here, the aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural…
Transformer and its variants have shown great potential for various vision tasks in recent years, including image classification, object detection and segmentation. Meanwhile, recent studies also reveal that with proper architecture design,…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Tracking of moving objects is crucial to security systems and networks. Given a graph $G$, terminal vertices $s$ and $t$, and an integer $k$, the \textsc{Tracking Paths} problem asks whether there exists at most $k$ vertices, which if…
We introduce several novel and computationally efficient methods for detecting "core--periphery structure" in networks. Core--periphery structure is a type of mesoscale structure that includes densely-connected core vertices and…
We introduce the graphlet decomposition of a weighted network, which encodes a notion of social information based on social structure. We develop a scalable inference algorithm, which combines EM with Bron-Kerbosch in a novel fashion, for…
Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded…
The success of Google's Pregel framework in distributed graph processing has inspired a surging interest in developing Pregel-like platforms featuring a user-friendly "think like a vertex" programming model. Existing Pregel-like systems…
In an edge modification problem, we are asked to modify at most $k$ edges to a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A…