# Scale-free network topology and multifractality in a weighted planar stochastic lattice

@article{Hassan2010ScalefreeNT, title={Scale-free network topology and multifractality in a weighted planar stochastic lattice}, author={M. Kamrul Hassan and M. Zahedul Hassan and Neeaj I. Pavel}, journal={New Journal of Physics}, year={2010}, volume={12}, pages={093045} }

We propose a weighted planar stochastic lattice (WPSL) formed by the random sequential partition of a plane into contiguous and non-overlapping blocks and we find that it evolves following several non-trivial conservation laws, namely is independent of time ∀n, where xi and yi are the length and width of the ith block. Its dual on the other hand, obtained by replacing each block with a node at its centre and the common border between blocks with an edge joining the two vertices, emerges as a…

## 17 Citations

### A weighted planar stochastic lattice with scale-free, small-world and multifractal properties

- MathematicsChaos, Solitons & Fractals
- 2022

### Scale-free coordination number disorder and multifractal size disorder in weighted planar stochastic lattice

- Mathematics
- 2011

The square lattice is perhaps the simplest cellular structure. In this work, however, we investigate the various structural and topological properties of the kinetic and stochastic counterpart of the…

### Multi-multifractality and dynamic scaling in stochastic porous lattice

- MathematicsThe European Physical Journal Special Topics
- 2021

In this article, we extend the idea of stochastic dyadic Cantor set to weighted planar stochastic lattice that leads to a stochastic porous lattice. The process starts with an initiator which we…

### Percolation on a multifractal scale-free planar stochastic lattice and its universality class.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

The results suggest that the percolation on WPSL belong to a separate universality class than on all other planar lattices.

### Contact process on weighted planar stochastic lattice

- Computer ScienceJournal of Statistical Mechanics: Theory and Experiment
- 2022

The critical behavior of the disordered system using extensive simulations shows the critical behavior is distinct from that on a regular lattice, suggesting it belongs to a different universality class.

### Dynamic scaling, data-collapse and self-similarity in Barabási–Albert networks

- Computer ScienceArXiv
- 2011

In this paper, we show that if each node of the Barabási–Albert (BA) network is characterized by the generalized degree q, i.e. the product of their degree k and the square root of their respective…

### Kinetic-exchange-like opinion dynamics in complex networks: roles of the dimensionality and local interaction topology

- PhysicsThe European Physical Journal B
- 2018

We study a kinetic-exchange-like opinion dynamics model with both positive and negative interactions in various complex networks. The control parameter p ∈ [0, 1] denotes the probability of the…

### Degree Distribution, Rank-size Distribution, and Leadership Persistence in Mediation-Driven Attachment Networks

- MathematicsArXiv
- 2016

### Dynamic scaling, data-collapse and self-similarity in mediation-driven attachment networks

- Computer ScienceChaos, Solitons & Fractals
- 2020

### Converting network–unlike data into complex networks: problems and prospective

- Computer ScienceJournal of Physics: Conference Series
- 2020

The algorithm models coarse-graining and area-like linking and forms thoroughly output structures of really complex topologies with intrinsic scale-free and small world properties and is considered as a promising approach to study more complex systems of the real world.

## References

SHOWING 1-10 OF 22 REFERENCES

### Emergence of scaling in random networks

- Computer ScienceScience
- 1999

A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

### Contact process on a Voronoi triangulation.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

The results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice, i.e., that of directed percolation.

### Understanding search trees via statistical physics

- Computer Science, PhysicsPramana
- 2005

It is shown that the probability distributions of extreme observables associated with a random search tree such as the height and the balanced height of a tree have a travelling front structure and the mechanism of this phase transition is generic.

### The Structure and Function of Complex Networks

- Computer ScienceSIAM Rev.
- 2003

Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

### Comment on "Kinematic scaling and crossover to scale invariance in martensite growth"

- MathematicsPhysical review letters
- 1996

These findings disagree with the ordinary scaling behavior of the segment length distribution reported in [1], and are equivalent to a stochastic process where seeds appear uniformly in space with unit rate, and grow with infinite velocity in the x or the y directions with equal probabilities.

### Kinematic scaling and crossover to scale invariance in martensite growth.

- Materials SciencePhysical review letters
- 1995

The results provide a method to compute dynamic quantities (v or I) from static optical micrographs of martensite grains and represent a novel example of a flow towards self-organized criticality.

### Scaling and multiscaling in models of fragmentation.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1994

A simple geometric model which describes the kinetics of fragmentation of d-dimensional objects and shows a simple scaling behavior in the long-time limit is introduced.

### Relation between grain shape and fractal properties in random Apollonian packing with grain rotation.

- Materials SciencePhysical review letters
- 2008

The constraining length D_c is identified that limits growth of the grain during the packing process and it is found that a universal relation exists between grain shape and the scaling properties of the system.

### Anderson Transitions

- Physics
- 2007

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term “Anderson transition” is understood in a broad sense, including both…