相关论文: On a composition of digraphs

A biological regulatory network can be modeled as a discrete function that contains all available information on network component interactions. From this function we can derive a graph representation of the network structure as well as of…

We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers. In particular, we prove the homotopy…

The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models,…

A family of graphs optimized as the topologies for supercomputer interconnection networks is proposed. The special needs of such network topologies, minimal diameter and mean path length, are met by special constructions of the weight…

Partition of unity methods (PUMs) on graphs represent straightforward and remarkably adaptable auxiliary techniques for graph signal processing. By relying solely on the intrinsic graph structure, we propose the generation of a partition of…

A unit disk graph is the intersection graph of disks of equal radii in the plane. The class of unit disk graphs is hereditary, and therefore admits a characterization in terms of minimal forbidden induced subgraphs. In spite of quite active…

Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…

Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…

The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…

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…

In this study, we performed comprehensive morphological investigations of the spontaneous formations of effective network structures among elements in coupled logistic maps, specifically with a delayed connection change. Our proposed model…

In network theory, a triad census is a method designed to categorize and enumerate the various types of subgraphs with three nodes and their connecting edges within a network. Triads serve as fundamental building blocks for comprehending…

We introduce torsoids, a canonical structure in matching covered graphs, corresponding to the bricks and braces of the graph. This allows a more fine-grained understanding of the structure of finite and infinite directed graphs with respect…

We give a recursion formula to generate all equivalence classes of biconnected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We give a linear map to produce a connected graph with say, u,…

We characterise the structure of those graphs of a given order which maximise the number of connected induced subgraphs for seven different graph classes, each with other prescribed parameters like minimum degree, independence number,…

Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…

Complex networks topologies present interesting and surprising properties, such as community structures, which can be exploited to optimize communication, to find new efficient and context-aware routing algorithms or simply to understand…

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems…

Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the…