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Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the…
Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list of topological invariants which combines the second…
The availability of network datasets advances research in network science, machine learning and related fields by enabling empirical analyses and their reproducibility, algorithm development, model validation and benchmarking. Existing…
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected…
Spatial dependency and spatial embedding are basic physical properties of many phenomena modeled by networks. The most indicated computational environment to deal with spatial information is to use Georeferenced Information System (GIS) and…
A relational structure R is ultrahomogeneous if every isomorphism of finite induced substructures of R extends to an automorphism of R. We classify the ultrahomogeneous finite binary relational structures with one asymmetric binary relation…
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…
We consider data structures for graphs where we maintain a subset of the nodes called sites, and allow proximity queries, such as asking for the closest site to a query node, and update operations that enable or disable nodes as sites. We…
Given any complex directed network, a set of acyclic subgraphs - the hierarchical backbone of the network - can be extracted that will provide valuable information about its hierarchical structure. The current paper presents how the…
Motivated by the bootstrap percolation process for graphs, we define a new, high-order generalisation to $k$-uniform hypergraphs, in which we infect $j$-sets of vertices for some integer $1\le j \le k-1$. We investigate the smallest…
The concept of structured occurrence nets is an extension of that of occurrence nets which are directed acyclic graphs that represent causality and concurrency information concerning a single execution of a distributed system. The formalism…
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…
Understanding emerging areas of a multidisciplinary research field is crucial for researchers,policymakers and other stakeholders. For them a knowledge structure based on longitudinal bibliographic data can be an effective instrument. But…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
Hypergraphs are characterized by complex topological structure, representing higher-order interactions among multiple entities through hyperedges. Lately, hypergraph-based deep learning methods to learn informative data representations for…
We impose a rather unknown algebraic structure called a `hyperstructure' to the underlying space of an affine algebraic group scheme. This algebraic structure generalizes the classical group structure and is canonically defined by the…
An Euler tour in a hypergraph (also called a rank-2 universal cycle or 1-overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, we define a covering $k$-hypergraph to be a non-empty…
Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their…