dorsal/arxiv
View SchemaOptimal Paths in Complex Networks with Correlated Weights: The World-wide Airport Network
| Authors | Zhenhua Wu, Lidia A. Braunstein, Vittoria Colizza, Reuven Cohen, Shlomo Havlin, H. Eugene Stanley |
|---|---|
| Categories | |
| ArXiv ID | physics/0609241 |
| URL | https://arxiv.org/abs/physics/0609241 |
| DOI | 10.1103/PhysRevE.74.056104 |
Abstract
We study complex networks with weights, $w_{ij}$, associated with each link connecting node $i$ and $j$. The weights are chosen to be correlated with the network topology in the form found in two real world examples, (a) the world-wide airport network, and (b) the {\it E. Coli} metabolic network. Here $w_{ij} \sim x_{ij} (k_i k_j)^\alpha$, where $k_i$ and $k_j$ are the degrees of nodes $i$ and $j$, $x_{ij}$ is a random number and $\alpha$ represents the strength of the correlations. The case $\alpha > 0$ represents correlation between weights and degree, while $\alpha < 0$ represents anti-correlation and the case $\alpha = 0$ reduces to the case of no correlations. We study the scaling of the lengths of the optimal paths, $\ell_{\rm opt}$, with the system size $N$ in strong disorder for scale-free networks for different $\alpha$. We calculate the robustness of correlated scale-free networks with different $\alpha$, and find the networks with $\alpha < 0$ to be the most robust networks when compared to the other values of $\alpha$. We propose an analytical method to study percolation phenomena on networks with this kind of correlation. We compare our simulation results with the real world-wide airport network, and we find good agreement.
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"abstract": "We study complex networks with weights, $w_{ij}$, associated with each link\nconnecting node $i$ and $j$. The weights are chosen to be correlated with the\nnetwork topology in the form found in two real world examples, (a) the\nworld-wide airport network, and (b) the {\\it E. Coli} metabolic network. Here\n$w_{ij} \\sim x_{ij} (k_i k_j)^\\alpha$, where $k_i$ and $k_j$ are the degrees of\nnodes $i$ and $j$, $x_{ij}$ is a random number and $\\alpha$ represents the\nstrength of the correlations. The case $\\alpha \u003e 0$ represents correlation\nbetween weights and degree, while $\\alpha \u003c 0$ represents anti-correlation and\nthe case $\\alpha = 0$ reduces to the case of no correlations. We study the\nscaling of the lengths of the optimal paths, $\\ell_{\\rm opt}$, with the system\nsize $N$ in strong disorder for scale-free networks for different $\\alpha$. We\ncalculate the robustness of correlated scale-free networks with different\n$\\alpha$, and find the networks with $\\alpha \u003c 0$ to be the most robust\nnetworks when compared to the other values of $\\alpha$. We propose an\nanalytical method to study percolation phenomena on networks with this kind of\ncorrelation. We compare our simulation results with the real world-wide airport\nnetwork, and we find good agreement.",
"arxiv_id": "physics/0609241",
"authors": [
"Zhenhua Wu",
"Lidia A. Braunstein",
"Vittoria Colizza",
"Reuven Cohen",
"Shlomo Havlin",
"H. Eugene Stanley"
],
"categories": [
"physics.soc-ph",
"cond-mat.stat-mech",
"physics.comp-ph",
"physics.data-an"
],
"doi": "10.1103/PhysRevE.74.056104",
"title": "Optimal Paths in Complex Networks with Correlated Weights: The World-wide Airport Network",
"url": "https://arxiv.org/abs/physics/0609241"
},
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