We study a general model of random dynamical simplicial complexes and derive formula for the asymptotic degree distribution. This generalises results number existing models, including Apollonian networks weighted recursive tree. It also confirms on scale-free nature complex quantum network manifolds in dimensions d>2, special types geometry with Flavour models studied physics literature by Bian...

The sanction against the insolvent debtor in Etruscan law – In society, according to a historiographical trend that begins with Aristotle, there was punished public redicule exposure. This punishment, apparently not incisive, be understood needs correlated legislation on perjury, preserved by Maurus Servius Honoratus, and many other Roman, Greek laws of ancient peoples. I will highlight Dionysi...

Spatially constrained planar networks are frequently encountered in real-life systems. In this paper, based on a space-filling disk packing we propose a minimal model for spatial maximal planar networks, which is similar to but different from the model for Apollonian networks (Andrade et al 2005 Phys. Rev. Lett. 94 018702). We present an exhaustive analysis of various properties of our model, a...

We study the heavy path decomposition of conditional Galton-Watson trees. In astandard Galton-Watson tree conditional on its size n, we order all children by their subtree sizes,from large (heavy) to small. A node is marked if it is among the k heaviest nodes among its siblings.Unmarked nodes and their subtrees are removed, leaving only a tree of marked nodes, which we callthe k...

Experimentally observed complex networks are often scale-free, small-world and have an unexpectedly large number of small cycles. An Apollonian network is one notable example a model simultaneously having all three these properties. This constructed by deterministic procedure consequentially splitting triangle into smaller triangles. In this paper, similar construction based on the consequentia...

Andre M. C. Souza1,2 and Hans Herrmann3,4 1Institut für Computerphysik, Universität Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany 2Departamento de Fisica, Universidade Federal de Sergipe, 49100-000 Sao Cristovao-SE, Brazil 3Computational Physics, IfB, ETH Hönggerberg, HIF E 12, CH-8093 Zürich, Switzerland 4Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza-CE, ...