Optimal Paths in Complex Networks with Correlated Weights: The World-wide Airport Network

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, ${\ell }_{\mathrm{opt}}$, 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.

References in corpus (1)

• Optimal Paths in Disordered Complex Networks

Cited by in corpus (10)

• Critical phenomena in complex networks
• Prominence and control: The weighted rich-club effect
• The International Trade Network: weighted network analysis and modelling
• Microdynamics in stationary complex networks
• How to make a fragile network robust and vice versa
• Global disease spread: statistics and estimation of arrival times
• Arrival Time Statistics in Global Disease Spread
• Transport on weighted Networks: when correlations are independent of degree
• Numerical evaluation of the upper critical dimension of percolation in scale-free networks
• Evolution equation for a model of surface relaxation in complex networks