Related papers: Prime stars multiplexes
An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…
It has been recognized that many complex dynamical systems in the real world require a description in terms of multiplex networks, where a set of common, mutually connected nodes belong to distinct network layers and play a different role…
The coexistence of multiple types of interactions within social, technological and biological networks has moved the focus of the physics of complex systems towards a multiplex description of the interactions between their constituents.…
We describe the emergence of the giant mutually connected component in networks of networks in which each node has a single replica node in any layer and can be interdependent only on its replica nodes in the interdependent layers. We prove…
Branching architecture characterizes numerous systems, ranging from synthetic (hyper)branched polymers and biomolecules such as lignin, amylopectin, and nucleic acids to tracheal and neuronal networks. Its ubiquity reflects the many…
An instance of the super-stable matching problem with incomplete lists and ties is an undirected bipartite graph $G = (A \cup B, E)$, with an adjacency list being a linearly ordered list of ties. Ties are subsets of vertices equally good…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
The robustness and resilience of complex systems are crucial for maintaining functionality amid disruptions or intentional attacks. Many such systems can be modeled as networks, where identifying structurally central nodes is essential for…
Identifying the most influential spreaders is important to understand and control the spreading process in a network. As many real-world complex systems can be modeled as multilayer networks, the question of identifying important nodes in…
We study the basic properties of a prime sum graph, which is a simple graph defined on $\mathbb N$ where two vertices are adjacent if and only if their sum is a prime number. Further, we investigate some specific structures that appear…
The paradigm of layered networks is used to describe many real-world systems -- from biological networks, to social organizations and transportation systems. Recently there has been much progress in understanding the general properties of…
We solve the weak percolation problem for multiplex networks with overlapping edges. In weak percolation, a vertex belongs to a connected component if at least one of its neighbors in each of the layers is in this component. This is a…
Modular networks, such as critical infrastructures, are often built from distinct, densely connected modules (e.g., cities) that are sparsely interconnected. When such networks are gradually and randomly disrupted under a percolation…
For any link and for any modulus $m$ we introduce an equivalence relation on the set of non-trivial m-colorings of the link (an m-coloring has values in Z/mZ). Given a diagram of the link, the equivalence class of a non-trivial m-coloring…
Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually…
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the…
Many, if not most network analysis algorithms have been designed specifically for single-relational networks; that is, networks in which all edges are of the same type. For example, edges may either represent "friendship," "kinship," or…
Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the…
Social scientists have long appreciated that relationships between individuals cannot be described from observing a single domain, and that the structure across domains of interaction can have important effects on outcomes of interest…