Self-similar disk packings as model spatial scale-free networks

Abstract

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 areas. A wide variety of topological and spatial properties of these systems are characterized. Their potential as models for networks of connected minima on energy landscapes is discussed.

Some Properties of Random Apollonian Networks

“…Specifically, the circle size distribution follows a power law with exponent around 1.3 [11]. Apollonian Networks (ANs) were introduced in [4] and independently in [20]. Zhou et al [35] introduced Random Apollonian Networks (RANs).…”

Recoverable DTN Routing Based on a Relay of Cyclic Message-Ferries on a MSQ Network

“…Complex network science that emerges at the beginning of the 21st century provides a new paradigm of network selforganization, e.g. based on recursive growing geometric rule for the division of a face [10], [11], [12], [13] or for the attachment which aims at a chosen edge [14], [15], [16] in a random or hierarchical selection. These self-organized networks including the MSQ network have a potential to be superior to the vulnerable scale-free network structure found in many real network systems [17], [18], such as Internet, WWW, power-grids, airline networks, etc.…”

Self-similar non-clustered planar graphs as models for complex networks

“…The first construction can be generalized to any d, see [10]. For d = 3, and related to the classical Apollonian packing of circles, Andrade et al and Doye and Massen introduced and studied the so called Apollonian networks [11,12]. These networks are also k-trees but new vertices are attached only to cliques which have never been selected in a former iteration.…”

“…Moreover, they are maximal planar graphs. The general case d ≥ 3, high dimensional Apollonian networks, was introduced in [12] and has been further studied in [13].…”