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Application-level peer-to-peer (P2P) network overlays are an emerging paradigm that facilitates decentralization and flexibility in the scalable deployment of applications such as group communication, content delivery, and data sharing.…
This paper revisits the robustness analysis and distributed ${ H}_\infty$ controller design for the platooning of connected vehicles. Recently, the relevant result subjected to the undirected topology has been studied, in the light of the…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
Transmission line failures in power systems propagate and cascade non-locally. This well-known yet counter-intuitive feature makes it even more challenging to optimally and reliably operate these complex networks. In this work we present a…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
Network renormalization has traditionally relied on spatial adjacency-grouping nearby nodes together, but this approach fails to capture the dynamical correlations that govern system-wide behavior in scale-free networks. We present a…
Complex network theory has recently been proposed as a promising tool for characterising interactions between aircraft, and their downstream effects. We here explore the problem of networks' topological predictability, i.e. the dependence…
Finding patterns in large highly connected datasets is critical for value discovery in business development and scientific research. This work focuses on the problem of subgraph matching on streaming graphs, which provides utility in a…
In these notes we study synchronizability of dynamical processes defined on complex networks as well as its interplay with network topology. Building from a recent work by Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)], we use a…
Incorporating spectral information to enhance Graph Neural Networks (GNNs) has shown promising results but raises a fundamental challenge due to the inherent ambiguity of eigenvectors. Various architectures have been proposed to address…
Graph convolutional networks have recently gained prominence in collaborative filtering (CF) for recommendations. However, we identify potential bottlenecks in two foundational components. First, the embedding layer leads to a latent space…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
This survey is two-fold. We first report new progress on the spectral extremal results on the Tur\'{a}n type problems in graph theory. More precisely, we shall summarize the spectral Tur\'{a}n function in terms of the adjacency spectral…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Statistical inference on graphs often proceeds via spectral methods involving low-dimensional embeddings of matrix-valued graph representations, such as the graph Laplacian or adjacency matrix. In this paper, we analyze the asymptotic…
AC optimal power flow (AC OPF) is a fundamental problem in power system operation and control. Accurately modeling the network physics via the AC power flow equations makes AC OPF a challenging nonconvex problem that results in significant…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific…
In this paper, subgraphs and complementary graphs are used to analyze the network synchronizability. Some sharp and attainable bounds are provided for the eigenratio of the network structural matrix, which characterizes the network…
The state-of-the-art topologies of datacenter networks are fixed, based on electrical switching technology, and by now, we understand their throughput and cost well. For the past years, researchers have been developing novel optical…