相关论文: Contact graphs of disk packings as a model of spat…

The network of contacts in space-filling disk packings, such as the Apollonian packing, are examined. These networks provide an interesting example of spatial scale-free networks, where the topology reflects the broad distribution of disk…

We introduce a new family of networks, the Apollonian networks, that are simultaneously scale-free, small world, Euclidean, space-filling and matching graphs. These networks have a wide range of applications ranging from the description of…

The family of planar graphs is a particularly important family and models many real-world networks. In this paper, we propose a principled framework based on the widely-known Apollonian packing process to generate new planar network, i.e.,…

In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…

Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…

There is a well-known relationship between the binary Pascal's triangle and Sierpinski triangle in which the latter obtained from the former by successive modulo 2 additions on one of its corners. Inspired by that, we define a binary…

In this paper we find an exact analytical expression for the number of spanning trees in Apollonian networks. This parameter can be related to significant topological and dynamic properties of the networks, including percolation, epidemic…

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…

Experimentally observed complex networks are often scale-free, small-world and have unexpectedly large number of small cycles. Apollonian network is one notable example of a model network respecting simultaneously having all three of these…

We review recent results on the topological properties of two spatial scale-free networks, the inherent structure and Apollonian networks. The similarities between these two types of network suggest an explanation for the scale-free…

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their…

Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…

We introduce a family of complex networks that interpolates between the Apollonian network and its binary version, recently introduced in [Phys. Rev. E \textbf{107}, 024305 (2023)], via random removal of nodes. The dilution process allows…

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

We study quasi-static deformation of dense granular packings. The packing is deformed by imposing external boundary conditions, which model engineering experiments such as shear and compression. We propose a two-dimensional network model of…

Physical networks are made of nodes and links that are physical objects embedded in a geometric space. Understanding how the mutual volume exclusion between these elements affects the structure and function of physical networks calls for a…

Empirical studies on the spatial structures in several real transport networks reveal that the distance distribution in these networks obeys power law. To discuss the influence of the power-law exponent on the network's structure and…

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski…

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…