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In quantum information theory there is a construction for quantum channels, appropriately called a quantum graph, that generalizes the confusability graph construction for classical channels in classical information theory. In this paper,…

Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…

We present a unified framework for path-parametric planning and control. This formulation is universal as it standardizes the entire spectrum of path-parametric techniques -- from traditional path following to more recent contouring or…

In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…

Long-range interactions are essential for the correct description of complex systems in many scientific fields. The price to pay for including them in the calculations, however, is a dramatic increase in the overall computational costs.…

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…

Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…

The modelling of discrete regulatory networks combines a graph specifying the pairwise influences between the variables of the system, and a parametrisation from which can be derived a discrete transition system. Given the influence graph…

Graph transformers are a recent advancement in machine learning, offering a new class of neural network models for graph-structured data. The synergy between transformers and graph learning demonstrates strong performance and versatility…

Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…

Modern computer networks support interesting new routing models in which traffic flows from a source s to a destination t can be flexibly steered through a sequence of waypoints, such as (hardware) middleboxes or (virtualized) network…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…

Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…

Traversals of data structures are ubiquitous in programming. Consequently, it is important to be able to characterise those structures that are traversable and understand their algebraic properties. Traversable functors have been…

We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…

The value proposition of a dataset often resides in the implicit interconnections or explicit relationships (patterns) among individual entities, and is often modeled as a graph. Effective visualization of such graphs can lead to key…

Dynamic algorithm selection aims to exploit the complementarity of multiple optimization algorithms by switching between them during the search. While these kinds of dynamic algorithms have been shown to have potential to outperform their…

Arrival of multicore systems has enforced a new scenario in computing, the parallel and distributed algorithms are fast replacing the older sequential algorithms, with many challenges of these techniques. The distributed algorithms provide…

We propose a novel sequence prediction method for sequential data capturing node traversals in graphs. Our method builds on a statistical modelling framework that combines multiple higher-order network models into a single multi-order…

Network service providers and customers are often concerned with aggregate performance measures that span multiple network paths. Unfortunately, forming such network-wide measures can be difficult, due to the issues of scale involved. In…