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Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs…
We describe the structure of triconnected graph with the help of its decomposition by 3-cutsets. We divide all 3-cutsets of a triconnected graph into rather small groups with a simple structure, named complexes. The detailed description of…
In the present paper we discuss the clustering procedure in the case where instead of a single metric we have a family of metrics. In this case we can obtain a partially ordered graph of clusters which is not necessarily a tree. We discuss…
We show that maximal families of mutually unbiased bases are characterized in all dimensions by partitioned unitary error bases, up to a choice of a family of Hadamards. Furthermore, we give a new construction of partitioned unitary error…
Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits.…
Research on structure determination and parameter estimation of hierarchical Archimedean copulas (HACs) has so far mostly focused on the case in which all appearing Archimedean copulas belong to the same Archimedean family. The present work…
A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…
Recently, deep supervised hashing methods have become popular for large-scale image retrieval task. To preserve the semantic similarity notion between examples, they typically utilize the pairwise supervision or the triplet supervised…
We study the use of local heuristics to determine spanning subgraphs for use in the dissemination of information in complex networks. We introduce two different heuristics and analyze their behavior in giving rise to spanning subgraphs that…
This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also…
Recently, hashing methods have been widely used in large-scale image retrieval. However, most existing hashing methods did not consider the hierarchical relation of labels, which means that they ignored the rich information stored in the…
In this paper new infinite families of linear binary completely transitive codes are presented. They have covering radius $\rho = 3$ and 4, and are a half part of the binary Hamming and the binary extended Hamming code of length $n=2^m-1$…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
The puncturing and shortening technique are two important approaches to constructing new linear codes from old ones. In the past 70 years, a lot of progress on the puncturing technique has been made, and many works on punctured linear codes…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
The relationship between Heyting algebras (HA) and semirings is explored. A new class of HAs called Symmetric Heyting algebras (SHAs) is proposed, and a necessary condition on SHAs to be consider semirings is given. We define a new…
Given a hypergraph $\mathcal{H}$, we introduce a new class of evaluation toric codes called edge codes derived from $\mathcal{H}$. We analyze these codes, focusing on determining their basic parameters. We provide estimations for the…
Assessing the accuracy of the output of causal discovery algorithms is crucial in developing and comparing novel methods. Common evaluation metrics such as the structural Hamming distance are useful for assessing individual links of causal…
Separable codes were introduced to provide protection against illegal redistribution of copyrighted multimedia material. Let $\mathcal{C}$ be a code of length $n$ over an alphabet of $q$ letters. The descendant code ${\sf…
In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are…