Related papers: Scale-free networks embedded in fractal space
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest…
Recent advances in deep learning have transformed many fields by introducing generic embedding spaces, capable of achieving great predictive performance with minimal labeling effort. The geology field has not yet met such success. In this…
Complex networks across various fields are often considered to be scale free -- a statistical property usually solely characterized by a power-law distribution of the nodes' degree $k$. However, this characterization is incomplete. In…
Cascading breakdowns of real networks are severe accidents in recent years, such as the blackouts of the power transportation networks in North America. In this paper, we study the effects of geographical structure on the cascading…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing…
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
Random walks are one of the best investigated dynamical processes on graphs. A particularly fascinating phenomenon is the scaling relationship of fluctuations $\sigma $ with the average flux $\langle f \rangle $. Here we analyze how network…
We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…
The coupling of scale-free networks with mobile unstructured networks is certainly unusual. In mobile networks, connections active at a given instant are constrained by the geographical distribution of mobile nodes, and by the limited…
Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to…
Every route of a transport network approaching equilibrium can be represented by a vector of Euclidean space which length quantifies its segregation from the rest of the graph. We have empirically observed that the distribution of lengths…
Information propagation characterizes how input correlations evolve across layers in deep neural networks. This framework has been well studied using mean-field theory, which assumes infinitely wide networks. However, these assumptions…
Many complex systems are organized in the form of a network embedded in space. Important examples include the physical Internet infrastucture, road networks, flight connections, brain functional networks and social networks. The effect of…
Spatial networks of land cover are well-described by power law rank-size distributions. Continuous field proxies for human settlements, agriculture and forest cover have similar spatial scaling properties spanning 4 to 5 orders of…
We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an…