Number of items: **4**.

## L

Leicht, Elizabeth,

Holme, Petter and

Newman, Mark
(2006)

*Vertex similarity in networks.*
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 73 (2).
pp. 1-10.
Link to full text available through this repository.

- Abstract
We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network. We test our similarity measure on computer-generated networks for which the expected results are known, and on a number of real-world networks.

- Item type
- Article
- Subject(s)
- Complexity
- Uncontrolled keywords
- Disordered Systems and Neural Networks; Data Analysis; Statistics and Probability
- Centre
- CABDyN Complexity Centre

López, Eduardo,

Buldyrev, Sergey,

Braunstein, Lidia,

Havlin, Shlomo and

Stanley, Eugene
(2005)

*Possible connection between the optimal path and flow in percolation clusters.*
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 72 (5).
pp. 6131-6137.
Link to full text available through this repository.

- Abstract
We study the behavior of the optimal path between two sites separated by a distance r on a d-dimensional lattice of linear size L with weight assigned to each site. We focus on the strong disorder limit, i.e., when the weight of a single site dominates the sum of the weights along each path. We calculate the probability distribution P(ellrm optr,L) of the optimal path length ellrm opt, and find for rll L a power law decay with ellrm opt, characterized by exponent grm opt. We determine the scaling form of P(ellrm optr,L) in two- and three-dimensional lattices. To test the conjecture that the optimal paths in strong disorder and flow in percolation clusters belong to the same universality class, we study the tracer path length ellrm tr of tracers inside percolation through their probability distribution P(ellrm trr,L). We find that, because the optimal path is not constrained to belong to a percolation cluster, the two problems are different. However, by constraining the optimal paths to remain inside the percolation clusters in analogy to tracers in percolation, the two problems exhibit similar scaling properties.

- Item type
- Article
- Subject(s)
- Complexity
- Uncontrolled keywords
- Disordered Systems and Neural Networks; Statistical Mechanics
- Centre
- CABDyN Complexity Centre

López, Eduardo,

Parshani, Roni,

Cohen, Reuven,

Carmi, Shai and

Havlin, Shlomo
(2007)

*Limited path percolation in complex networks.*
Physical Review Letters, 99 (18).
p. 188701.
Link to full text available through this repository.

- Abstract
We study the stability of network communication after removal of a fraction q=1-p of links under the assumption that communication is effective only if the shortest path between nodes i and j after removal is shorter than aℓij(a≥1) where ℓij is the shortest path before removal. For a large class of networks, we find analytically and numerically a new percolation transition at p˜c=(κ0-1)(1-a)/a, where κ0≡⟨k2⟩/⟨k⟩ and k is the node degree. Above p˜c, order N nodes can communicate within the limited path length aℓij, while below p˜c, Nδ (δ<1) nodes can communicate. We expect our results to influence network design, routing algorithms, and immunization strategies, where short paths are most relevant.

- Item type
- Article
- Subject(s)
- Complexity
- Uncontrolled keywords
- Statistical Mechanics; Disordered Systems and Neural Networks; Complex Networks
- Centre
- CABDyN Complexity Centre

## W

Wu, Zhenhua,

López, Eduardo,

Braunstein, Lidia,

Buldyrev, Sergey,

Havlin, Shlomo and

Stanley, Eugene
(2005)

*Current Flow in Random Resistor Networks: The role of Percolation in Weak and Strong Disorder.*
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 71 (4).
Link to full text available through this repository.

- Abstract
We study the current flow paths between two edges in a random resistor network on a Ltimes L square lattice. Each resistor has resistance e ax, where x is a uniformly-distributed random variable and a controls the broadness of the distribution. We find (a) the scaled variable uequiv L/a nu, where nu is the percolation connectedness exponent, fully determines the distribution of the current path length ell for all values of u. For ugg 1, the behavior corresponds to the weak disorder limit and ell scales as ellsim L, while for ull 1, the behavior corresponds to the strong disorder limit with ellsim L dscriptsize opt, where dscriptsize opt = 1.22pm0.01 is the optimal path exponent. (b) In the weak disorder regime, there is a length scale xisim a nu, below which strong disorder and critical percolation characterize the current path.

- Item type
- Article
- Subject(s)
- Complexity
- Uncontrolled keywords
- Disordered Systems and Neural Networks; Materials Science
- Centre
- CABDyN Complexity Centre

This list was generated on **Sat Sep 21 00:21:01 2019 UTC**.