Study on the phase transition of the fractal scale-free networks

We explore the use of complex networks for understanding of the interaction of computer software applications written in the Java object-oriented language with the "library classes" that they use (those provided by the Java Runtime Environment) as, essentially, a merged network of classes. The dependence of the software on the library is quantified using a recently introduced model that identifies phases close to a second-order phase transition existing in scale-free networks. An example is given of a piece of software whose class network collapses without the presence of the library classes, providing validation of a novel structural coupling measure; R coupling . The structural properties of the merged software-Java class networks were found to correlate with the proportion of Java classes contained within the subset delimited by R coupling . A mechanism for the preservation of the software class network is also provided for the cases studied where the removal of the library classes does not cause collapse.

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Quantum phase transition of the transverse-field quantum Ising model on scale-free networks

Physical Review E ◽

10.1103/physreve.91.012146 ◽

2015 ◽

Vol 91 (1) ◽

Cited By ~ 3

Author(s):

Hangmo Yi

Keyword(s):

Phase Transition ◽

Ising Model ◽

Quantum Phase Transition ◽

Transverse Field ◽

Quantum Phase ◽

Scale Free ◽

Quantum Ising Model ◽

Scale Free Networks

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The contact process on scale-free networks evolving by vertex updating

Royal Society Open Science ◽

10.1098/rsos.170081 ◽

2017 ◽

Vol 4 (5) ◽

pp. 170081 ◽

Cited By ~ 6

Author(s):

Emmanuel Jacob ◽

Peter Mörters

Keyword(s):

Phase Transition ◽

Power Law ◽

Mathematical Proof ◽

Contact Process ◽

Network Size ◽

Mean Field Approximation ◽

Infection Rates ◽

Scale Free ◽

Power Law Exponent ◽

Scale Free Networks

We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all infection rates the infection survives for a long time, at least exponential in the network size, and a phase where for sufficiently small infection rates extinction occurs quickly, at most polynomially in the network size. The phase transition occurs when the power-law exponent crosses the value four. This behaviour is in contrast with that of the contact process on the corresponding static model, where there is no phase transition, as well as that of a classical mean-field approximation, which has a phase transition at power-law exponent three. The new observation behind our result is that temporal variability of networks can simultaneously increase the rate at which the infection spreads in the network, and decrease the time at which the infection spends in metastable states.

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