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 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...
متن کاملCritical phenomena in heterogeneous k-core percolation.
k-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analyzing the resilience of a network under random damage, an extension of this model is introduced, allowing different vertices to have their own degree of resilience. This extension is named heterogeneous k-core percolation and it is characterized by several...
متن کاملOn k-Sets in Four Dimensions
We show, with an elementary proof, that the number of halving simplices in a set of n points in R4 in general position is O(n4−2/45). This improves the previous bound of O(n4−1/13 4 ). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2008
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.78.022101