Related papers: Structural reducibility of hypergraphs
In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…
Extracting understanding from the growing ``sea'' of biological and socio-economic data is one of the most pressing scientific challenges facing us. Here, we introduce and validate an unsupervised method that is able to accurately extract…
This work presents some outcomes of a theoretical investigation of incompressible high-order networks defined by a generalized graph representation. We study some of their network topological properties and how these may be related to…
Understanding cooperation in social dilemmas requires models that capture the complexity of real-world interactions. While network frameworks have provided valuable insights to model the evolution of cooperation, they are unable to encode…
Dynamic systems that consist of a set of interacting elements can be abstracted as temporal networks. Recently, higher-order patterns that involve multiple interacting nodes have been found crucial to indicate domain-specific laws of…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
This article defines a partial order structure to study the relationship between levels and contents of conscious subjective experience in a single mathematical set-up. We understand phenomenal structure as extrapolated relationships among…
Heterogeneous and complex networks represent intertwined interactions between real-world elements or agents. Determining the multi-scale mesoscopic organization of clusters and intertwined structures is still a fundamental and open problem…
Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
In network science, collective dynamics of complex systems are typically modelled as (nonlinear, often including many-body) vertex-level update rules evolving over a graph interaction structure. In recent years, frameworks that explicitly…
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…
Understanding and predicting mobility dynamics in transportation networks is critical for infrastructure planning, resilience analysis, and traffic management. Traditional graph-based models typically assume memoryless movement, limiting…
Understanding how cooperative behaviours can emerge from competitive interactions is an open problem in biology and social sciences. While interactions are usually modelled as pairwise networks, the units of many real-world systems can also…
Document structure analysis, such as zone segmentation and table recognition, is a complex problem in document processing and is an active area of research. The recent success of deep learning in solving various computer vision and machine…