Related papers: Prime stars multiplexes
A simple and connected $n$-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers $1, 2, 3,\ldots, n$, such that adjacent vertices have relatively prime labels. We will present previously…
The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multi-layer networks, i.e. networks where each layer stands for…
A simple $n$-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers $1, 2, 3,\ldots, n$ such that adjacent vertices have relatively prime labels. We will present previously unknown prime vertex…
We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling…
Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social…
The multiplex network growth literature has been confined to homogeneous growth hitherto, where the number of links that each new incoming node establishes is the same across layers. This paper focuses on heterogeneous growth. We first…
Computing layer similarities is an important way of characterizing multiplex networks because various static properties and dynamic processes depend on the relationships between layers. We provide a taxonomy and experimental evaluation of…
Inter-layer synchronization is a distinctive process of multiplex networks whereby each node in a given layer undergoes a synchronous evolution with all its replicas in other layers, irrespective of whether or not it is synchronized with…
Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the…
A prime labeling of a graph with $n$ vertices is a labeling of its vertices with distinct integers from $\{1, 2,\ldots , n\}$ in such a way that the labels of any two adjacent vertices are relatively prime. T. Varkey conjectured that ladder…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
A prime labeling on a graph of order $m$ is an assignment of $\{ 1, 2, \ldots, m \}$ to the vertices of the graph such that each pair of adjacent vertices has coprime labels. The ladder of order $2n$ is the $2 \times n$ grid graph graph…
In multiplex networks, cycles cannot be characterized only by their length, as edges may occur in different layers in different combinations. We define a classification of cycles by the number of edges in each layer and the number of…
From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different networks (layers).…
We introduce a methodology based on averaging similarity matrices with the aim of integrating the layers of a multiplex network into a single monoplex network. Multiplex networks are adopted for modelling a wide variety of real-world…
There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. This is the case for example in social networks where each individual node has different kind of social ties or…
Many real-world network are multilayer, with nontrivial correlations across layers. Here we show that these correlations amplify geometry in networks. We focus on mutual clustering--a measure of the amount of triangles that are present in…
Multilayer network analysis has become a vital tool for understanding different relationships and their interactions in a complex system, where each layer in a multilayer network depicts the topological structure of a group of nodes…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
A coprime labeling of a simple graph of order $n$ is a labeling in which adjacent vertices are given relatively prime labels, and a graph is prime if the labels used can be taken to be the first $n$ positive integers. In this paper, we…