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 (26)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Epidemic spreading in scale-free networks
• The architecture of complex weighted networks
• Random graphs with arbitrary degree distributions and their applications
• Network robustness and fragility: Percolation on random graphs
• Resilience of the Internet to random breakdowns
• The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
• Breakdown of the Internet under intentional attack
• Scale-Free Networks are Ultrasmall
• Dynamics of market correlations: Taxonomy and portfolio analysis
• Global organization of metabolic fluxes in the bacterium, Escherichia coli
• Weighted evolving networks: coupling topology and weights dynamics
• Statistical Analysis of Airport Network of China
• Weighted Evolving Networks
• Topology of correlation based minimal spanning trees in real and model markets
• Stability and topology of scale-free networks under attack and defense strategies
• General Dynamics of Topology and Traffic on Weighted Technological Networks
• Optimal Paths in Disordered Complex Networks
• Anomalous Transport in Complex Networks
• Weighted Scale-Free Networks with Stochastic Weight Assignments
• Current Flow in Random Resistor Networks: The Role of Percolation in Weak and Strong Disorder
• Effect of Disorder Strength on Optimal Paths in Complex Networks
• Statistics of Weighted Networks
• Scale-Free Networks Emerging from Weighted Random Graphs

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• Microdynamics in stationary complex networks
• How to make a fragile network robust and vice versa
• Global disease spread: statistics and estimation of arrival times
• Influence of autocorrelation on the topology of the climate network
• Q-based design equations for resonant metamaterials and experimental validation
• Biased Percolation on Scale-free Networks
• Arrival Time Statistics in Global Disease Spread
• Transport on weighted Networks: when correlations are independent of degree
• Epidemic spreading driven by biased random walks
• Numerical evaluation of the upper critical dimension of percolation in scale-free networks
• Correlations in complex networks under attack
• Distributed flow optimization and cascading effects in weighted complex networks
• Preferential Attachment in the Interaction between Dynamically Generated Interdependent Networks
• Evolution equation for a model of surface relaxation in complex networks
• Percolation on bipartite scale-free networks
• Critical Cooperation Range to Improve Spatial Network Robustness
• Estimating epidemic arrival times using linear spreading theory