Related papers: Link persistence and conditional distances in mult…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…
We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary…
It is known that for a variety of choices of metrics, including the standard bottleneck distance, the space of persistence diagrams admits geodesics. Typically these existence results produce geodesics that have the form of a convex…
Persistent homology has been widely used to discover hidden topological structures in data across various applications, including music data. To apply persistent homology, a distance or metric must be defined between points in a point cloud…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Biological molecules can form hydrogen bonds between nearby residues, leading to helical secondary structures. The associated reduction of configurational entropy leads to a temperature dependence of this effect: the "helix-coil…
Real-world networks exhibit universal structural properties such as sparsity, small-worldness, heterogeneous degree distributions, high clustering, and community structures. Geometric network models, particularly Random Hyperbolic Graphs…
Multiplex networks are a representation of real-world complex systems as a set of entities (i.e. nodes) connected via different types of connections (i.e. layers). The observed connections in these networks may not be complete and the link…
Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural…
Multiplex graphs capture diverse relations among shared nodes. Most predictors either collapse layers or treat them independently. This loses crucial inter-layer dependencies and struggles with scalability. To overcome this, we frame…
A multiplex is a collection of network layers, each representing a specific type of edges. This appears to be a genuine representation for many real-world systems. However, due to a variety of potential factors, such as limited budget and…
The Renormalization Group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric…
Multiplex networks are receiving increasing interests because they allow to model relationships between networked agents on several layers simultaneously. In this supplementary material for the paper "Navigability of interconnected networks…
The hierarchy and proximity are key dimensions of urban relational processes, but their interplay in shaping intercity interactions and the underlying structures of city systems remain unclear. We develop a novel geometric model of city…
Complex systems are characterized by multiple spatial and temporal scales. A natural framework to capture their multiscale nature is that of multilayer networks, where different layers represent distinct physical processes that often…
The entities of real-world networks are connected via different types of connections (i.e. layers). The task of link prediction in multiplex networks is about finding missing connections based on both intra-layer and inter-layer…
Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific…
The self-similarity of complex systems has been studied intensely across different domains due to its potential applications in system modeling, complexity analysis, etc., as well as for deep theoretical interest. Existing studies rely on…