Related papers: Structural properties of spatially embedded networ…
In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes…
We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…
What is the dimension of a network? Here, we view it as the smallest dimension of Euclidean space into which nodes can be embedded so that pairwise distances accurately reflect the connectivity structure. We show that a recently proposed…
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree…
Recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems such as urban transport networks. In this paper, we study the response of real-world spatio-temporal networks to…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
In this paper, we study the probability that a dense network confined within a given geometry is fully connected. We employ a cluster expansion approach often used in statistical physics to analyze the effects that the boundaries of the…
The high computational complexity and increasing parameter counts of deep neural networks pose significant challenges for deployment in resource-constrained environments, such as edge devices or real-time systems. To address this, we…
The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most…
In this paper, we study the clustering properties of the Spatial Preferential Attachment (SPA) model. This model naturally combines geometry and preferential attachment using the notion of spheres of influence. It was previously shown in…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
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…
We consider two (2D) and three (3D) dimensional granular systems exposed to compression, and ask what is the influence of the number of physical dimensions on the properties of the interaction networks that spontaneously form as these…
Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…
Data clustering, the task of grouping observations according to their similarity, is a key component of unsupervised learning -- with real world applications in diverse fields such as biology, medicine, and social science. Often in these…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
We consider a three dimensional spatial network, where $N$ nodes are randomly distributed within a cube $L\times L\times L$. Each two nodes are connected if their mutual distance does not excess a given cutoff $a$. We analyse numerically…
Dimension in physical systems determines universal properties at criticality. Yet, the impact of structural perturbations on dimensionality remains largely unexplored. Here, we characterize the attraction basins of structural fixed points…
Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…