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

@article{Hassan2016DegreeDR, title={Degree Distribution, Rank-size Distribution, and Leadership Persistence in Mediation-Driven Attachment Networks}, author={Md. Kamrul Hassan and Liana Islam and Syed Arefinul Haque}, journal={ArXiv}, year={2016}, volume={abs/1611.04583} }

We investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with m randomly chosen neighbors of the mediator at each time step. We show that the degree distribution in such a mediation-driven attachment (MDA) network exhibits power-law P(k)∼k−γ(m) with a spectrum of exponents depending on m. To appreciate the contrast between MDA and Barabasi–Albert (BA) networks, we then discuss their rank-size distribution. To quantify how long a leader… Expand

#### 16 Citations

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

- Physics, Mathematics
- 2018

Recently, we have shown that if the $i$th node of the Barab\'{a}si-Albert (BA) network is characterized by the generalized degree $q_i(t)=k_i(t)t_i^\beta/m$, where $k_i(t)\sim t^\beta$ and $m$ are… Expand

Universality class of explosive percolation in Barabási-Albert networks

- Physics, Medicine
- Scientific Reports
- 2019

This work study explosive percolation in Barabási-Albert network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process finds that the critical exponents ν, α, β and γ for m > 1 are found to be independent not only of the value of m but also of PR and SR. Expand

Modelling and Analysis the Network Model Controlled by Mediation-Driven Attachment Rule

- Computer Science
- ICST
- 2020

The problem of modeling scale-free networks is considered and the dependence of the scaling factor of nodes degree distribution on the control parameter – the number of links associated with incoming nodes – is analyzed both analytically and by numerical simulation. Expand

Correlated copying in a hidden network model

- 2021

We introduce the concept of a hidden network model – a generative two-layer network in which an observed network evolves according to the structure of an underlying hidden layer. We apply the concept… Expand

The longest path in the Price model

- Physics, Mathematics
- Scientific Reports
- 2020

A reverse greedy path is defined and it is shown both analytically and numerically that this scales with the logarithm of the size of the network with a coefficient given by the number of edges added using random attachment. Expand

Heterogeneous node copying from hidden network structure

- Communications Physics
- 2021

Node copying is an important mechanism for network formation, yet most models assume uniform copying rules. Motivated by observations of heterogeneous triadic closure in real networks, we introduce… Expand

Elastic Scale-Free Networks Model Based on the Mediaton-Driven Attachment Rule

- Computer Science
- 2020 IEEE Third International Conference on Data Stream Mining & Processing (DSMP)
- 2020

Applying the copy-factor as the control parameter instead of traditionally used number of incoming links makes it possible to generate networks model, which combines the key benefits of mediation- driven attachment, such as indirect using the nodes degree, and elasticity,such as different relative growth rates for links and nodes. Expand

COVID-19 Should be Suppressed by Mixed Constraints -- from Simulations on Constrained Scale-Free Networks

- Computer Science, Physics
- ArXiv
- 2020

For quickly suppressing the number of infections, restrict W to less than 4 if the constraint to make m0 at most 1 is too strict, and set m0 to 4 or less works for quick reduction of infections according to the result. Expand

Infections May Not be Suppressed by Moderate Restriction of Contacts -- Simulated Expansions of Virus in Constrained Scale-Free Networks

- Physics
- 2020

Infection of virus is here simulated over human networks where the widths, defined as two constants representing the size of the contacting community, are constrained. In this model, the real-space… Expand

Scale-free Network-based Differential Evolution

- Computer Science
- ArXiv
- 2021

The novelties of this paper include a scale-free network-based population structure and a new mutation operator designed to fully utilize the neighborhood information provided by a scalefree structure to alleviate the drawbacks of premature convergence. Expand

#### References

SHOWING 1-10 OF 50 REFERENCES

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

- Mathematics, Computer Science
- ArXiv
- 2011

In this paper, we show that if each node of the Barabasi–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… Expand

Organization of growing random networks.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

The organizational development of growing random networks is investigated, and the combined age and degree distribution of nodes shows that old nodes typically have a large degree. Expand

Highly dispersed networks generated by enhanced redirection

- Mathematics, Physics
- 2014

We analyze growing networks that are built by enhanced redirection. Nodes are sequentially added and each incoming node attaches to a randomly chosen 'target' node with probability 1 − r, or to the… Expand

Scale-free network growth by ranking.

- Computer Science, Medicine
- Physical review letters
- 2006

A criterion of network growth that explicitly relies on the ranking of the nodes according to any prestige measure, be it topological or not is proposed, which may explain the frequency and robustness of scale-free degree distributions in real networks, as illustrated by the special case of the Web graph. Expand

Evolution of networks with aging of sites

- Physics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

It is found both from simulation and analytically that the network shows scaling behavior only in the region alpha<1, when alpha increases from -infinity to 0, and the exponent gamma of the distribution of connectivities grows from 2 to the value for the network without aging. Expand

Highly dispersed networks by enhanced redirection.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2013

A class of networks that grow by enhanced redirection is introduced, and each either attaches to a randomly chosen target node or to the parent of the target with probability r, where r is an increasing function of the degree of the parent. Expand

Scale-free networks via attaching to random neighbors

- Mathematics
- 2013

Preferential attachment is considered one of the key factors in the formation of scale-free networks. However, complete random attachment without a preferential mechanism can also generate scale-free… Expand

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

- Physics
- 2010

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… Expand

Duplication Models for Biological Networks

- Mathematics, Physics
- J. Comput. Biol.
- 2003

Combinatorial probabilistic methods are used to examine the evolution of graphs by node duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Expand

Topology of evolving networks: local events and universality

- Physics, Computer Science
- Physical review letters
- 2000

A continuum theory is proposed that predicts the connectivity distribution of the network describing the professional links between movie actors as well as the scaling function and the exponents, in good agreement with numerical results. Expand