Related papers: The Netsukuku network topology
We propose a mapping from fracture systems consisting of intersecting fracture sheets in three dimensions to an abstract network consisting of nodes and links. This makes it possible to analyze fracture systems with the methods developed…
This document describes the QSPN, the routing discovery algorithm used by Netsukuku. Through a deductive analysis the main proprieties of the QSPN are shown. Moreover, a second version of the algorithm, is presented.
In this paper, we introduce the foundation of a fractal topological space constructed via a family of nested topological spaces endowed with subspace topologies, where the number of topological spaces involved in this family is related to…
In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…
In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish some graph structures on fractal squares to reveal the…
In this paper we introduce new models of complex weighted networks sharing several properties with fractal sets: the deterministic non-homogeneous weighted fractal networks and the stochastic weighted fractal networks. Networks of both…
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
Blockchain technology holds promise for Web 3.0, but scalability remains a critical challenge. Here, we present a mathematical theory for a novel blockchain network topology based on fractal N-dimensional simplexes. This Hyper-simplex…
We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.
We introduce "fractalization", a procedure by which spin models are extended to higher-dimensional "fractal" spin models. This allows us to interpret type-II fracton phases, fractal symmetry-protected topological phases, and more, in terms…
We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the…
In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we…
A way to add an extra dimension is briefly discussed.
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
We introduce and use k-shell decomposition to investigate the topology of the Internet at the AS level. Our analysis separates the Internet into three sub-components: (a) a nucleus which is a small (~100 nodes) very well connected globally…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…
Fracton phases exhibit striking behavior which appears to render them beyond the standard topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter. Here, we explore fracton phases from the perspective of defect…
Starting from an isotropic configuration of intersecting, two-dimensional toric codes, we construct a fracton topological phase introduced in Ref. [26], which is characterized by immobile, point- like topological excitations ("fractons"),…