Related papers: Self-similar disk packings as model spatial scale-…
Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…
We find that transport on scale-free random networks depends strongly on degree-correlated network topologies whereas transport on Erd$\ddot{o}$s-R$\acute{e}$nyi networks is insensitive to the degree correlation. An approach for the tuning…
Random tilings or packings in the plane are characterized by a size distribution of individual elements (domains) and by the statistics of neighbor relations between the domains. Most systems occurring in nature or technology have a…
We consider Apollonian circle packings of a half Euclidean plane. We give necessary and sufficient conditions for two such packings to be related by a Euclidean similarity (that is, by translations, reflections, rotations and dilations) and…
We generalize the degree-organizational view of real-world networks with broad degree-distributions in a landscape analogue with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent…
An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
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.,…
Any space-filling packing of spheres can be cut by a plane to obtain a space-filling packing of disks. Here, we deal with space-filling packings generated using inversive geometry leading to exactly self-similar fractal packings. First, we…
Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome…
Self-assembly of chiral particles with an L-shape is explored by Monte-Carlo computer simulations in two spatial dimensions. For sufficiently high packing densities in confinement, a carpet-like texture emerges due to the interlocking of…
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…
Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks…
A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being…
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural…
A general relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks.…
The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force…
Different weighted scale-free networks show weights-topology correlations indicated by the non linear scaling of the node strength with node connectivity. In this paper we show that networks with and without weight-topology correlations can…
The topological structure resulting from the network of contacts between grains (contact network) is studied for very large samples of disorderly-packed monosized spheres with densities ranging from 0.58 to 0.64. The hierarchical…
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…