Abstract
In this work, we study explosive percolation (EP) in Barabási-Albert (BA) network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process. For m = 1 we find that the critical point tc = 1 which is the maximum possible value of the relative link density t; Hence we cannot have access to the other phase like percolation in one dimension. However, for m > 1 we find that tc decreases with increasing m and 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. It implies that they all belong to the same universality class like EP in the Erdös-Rényi network. Besides, the critical exponents obey the Rushbrooke inequality α + 2β + γ ≥ 2 but always close to equality. PACS numbers: 61.43.Hv, 64.60.Ht, 68.03.Fg, 82.70.Dd.
Highlights
Percolation is still studied in extenso even after more than 60 years of its first formulation[1,2,3,4,5,6,7]
It has been reported that random percolation (RP) in scale-free weighted planar stochastic lattice (WPSL) belongs to a universality class which is different from the unique universality class of all the known planar lattices[32,33]
Motivated by the role that the scale-free nature of the skeleton plays in percolation, we study two variants of explosive percolation” (EP), namely product rule (PR) and sum rule (SR) under Achlioptas process (AP), on scale-free BA networks whose nodes are born with degree m
Summary
We begin by discussing the construction process of the BA network. It starts by choosing a seed that may consists of m0 arbitrarily connected nodes where m0 has to be extremely small compared to the final size N of the network that we intend to grow. The total number of links in the BA networks of size N is approximately equal to mN since each node is born with degree m. The total degree is equal to 2 mN and the average degree of the BA network of size N is 2 m and for m = 1 it is a tree network Network grown in this way can be used as a skeleton provided the snapshots of the network in the same realization at different times are similar. If we measure the fraction of the nodes which have IHM values within a given class, which we call relative frequency, the resulting histogram plot for different m value is shown in Fig. The BA network for different m is significantly different albeit the exponent of the degree distribution is the same
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
