منابع مشابه
Dynamics of k-core percolation
In many network applications nodes are stable provided they have at least k neighbours, and a network of k-stable nodes is called a k-core. The vulnerability to random attack is characterized by the size of culling avalanches which occur after a randomly chosen k-core node is removed. Simulations of lattices in two, three and four dimensions, as well as small-world networks, indicate that power...
متن کاملExpansion for k-Core Percolation
The physics of k-core percolation pertains to those systems whose constituents require a minimum number of k connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from orientational ordering in solid ortho-para H2 mixtures to the onset of rigidity in barjoint networks to dynamical arrest in glass-forming liquids. Unlike ordinary (k=1...
متن کاملLong-range percolation in R
Let X be either Z or the points of a Poisson process in R of intensity 1. Given parameters r and p, join each pair of points of X within distance r independently with probability p. This is the simplest case of a ‘spreadout’ percolation model studied by Penrose [6], who showed that, as r → ∞, the average degree of the corresponding random graph at the percolation threshold tends to 1, i.e., the...
متن کاملLong-Range Percolation Mixing Time
We provide an estimate, sharp up to poly-logarithmic factors, of the asymptotically almost sure mixing time of the graph created by long-range percolation on the cycle of length N (Z/NZ). While it is known that the almost sure diameter drops from linear to poly-logarithmic as the exponent s decreases below 2 [4, 9], the almost sure mixing time drops from N only to N (up to poly-logarithmic fact...
متن کاملTricritical point in heterogeneous k-core percolation.
k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which e...
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2010
ISSN: 1742-6596
DOI: 10.1088/1742-6596/246/1/012019