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Robustness of oscillatory behavior in correlated networks.

Sasai T, Morino K, Tanaka G, Almendral JA, Aihara K - PLoS ONE (2015)

Bottom Line: The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree-degree correlations, is still unclear.Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity.Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.

View Article: PubMed Central - PubMed

Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

ABSTRACT
Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree-degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.

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Network reshuffling methods for changing the network assortativity.(a) The greedy edge-rewiring (GER) method [36]. The remaining degrees of the two connected node pairs, (j1, k1) and (j2, k2), are sorted in the descending order and relabeled as l1, l2, l3, and l4 so that l1 ≥ l2 ≥ l3 ≥ l4. The size of the node corresponds to its remaining degree. When making the network assortative, Case I is chosen if the current state is Case II or III. When making the network disassortative, Case III is chosen if the current state is Case I or II. (b) The stochastic edge-rewiring (SER) method [8]. The acceptance probability for edge rewiring is given by  where E(j, k) is the joint probability distribution for the remaining degrees of the two nodes in the end of a randomly chosen edge.
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pone.0123722.g002: Network reshuffling methods for changing the network assortativity.(a) The greedy edge-rewiring (GER) method [36]. The remaining degrees of the two connected node pairs, (j1, k1) and (j2, k2), are sorted in the descending order and relabeled as l1, l2, l3, and l4 so that l1 ≥ l2 ≥ l3 ≥ l4. The size of the node corresponds to its remaining degree. When making the network assortative, Case I is chosen if the current state is Case II or III. When making the network disassortative, Case III is chosen if the current state is Case I or II. (b) The stochastic edge-rewiring (SER) method [8]. The acceptance probability for edge rewiring is given by where E(j, k) is the joint probability distribution for the remaining degrees of the two nodes in the end of a randomly chosen edge.

Mentions: In the GER method, the edge rewiring is conducted based on the degrees of the connected node pairs. We sort the remaining degrees j1, j2, k1, and k2 in descending order and relabel them to l1, l2, l3 and l4 so that l1 ≥ l2 ≥ l3 ≥ l4. Fig 2(a) illustrates the three possibilities for separating the four nodes into two pairs of connected nodes. When increasing the assortativity coefficient, Case I is chosen to set the edges between the nodes with more similar degrees if the current state is Case II or III. When decreasing the assortativity coefficient, Case III is chosen to set an edge between the nodes with the largest and smallest degrees if the current state is Case I or II. We increase or decrease the assortativity coefficient by repeating the edge rewiring in a greedy way and continue until the assortativity coefficient is no longer changed. The assortativity coefficient r monotonically increases or decreases with this method.


Robustness of oscillatory behavior in correlated networks.

Sasai T, Morino K, Tanaka G, Almendral JA, Aihara K - PLoS ONE (2015)

Network reshuffling methods for changing the network assortativity.(a) The greedy edge-rewiring (GER) method [36]. The remaining degrees of the two connected node pairs, (j1, k1) and (j2, k2), are sorted in the descending order and relabeled as l1, l2, l3, and l4 so that l1 ≥ l2 ≥ l3 ≥ l4. The size of the node corresponds to its remaining degree. When making the network assortative, Case I is chosen if the current state is Case II or III. When making the network disassortative, Case III is chosen if the current state is Case I or II. (b) The stochastic edge-rewiring (SER) method [8]. The acceptance probability for edge rewiring is given by  where E(j, k) is the joint probability distribution for the remaining degrees of the two nodes in the end of a randomly chosen edge.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4403822&req=5

pone.0123722.g002: Network reshuffling methods for changing the network assortativity.(a) The greedy edge-rewiring (GER) method [36]. The remaining degrees of the two connected node pairs, (j1, k1) and (j2, k2), are sorted in the descending order and relabeled as l1, l2, l3, and l4 so that l1 ≥ l2 ≥ l3 ≥ l4. The size of the node corresponds to its remaining degree. When making the network assortative, Case I is chosen if the current state is Case II or III. When making the network disassortative, Case III is chosen if the current state is Case I or II. (b) The stochastic edge-rewiring (SER) method [8]. The acceptance probability for edge rewiring is given by where E(j, k) is the joint probability distribution for the remaining degrees of the two nodes in the end of a randomly chosen edge.
Mentions: In the GER method, the edge rewiring is conducted based on the degrees of the connected node pairs. We sort the remaining degrees j1, j2, k1, and k2 in descending order and relabel them to l1, l2, l3 and l4 so that l1 ≥ l2 ≥ l3 ≥ l4. Fig 2(a) illustrates the three possibilities for separating the four nodes into two pairs of connected nodes. When increasing the assortativity coefficient, Case I is chosen to set the edges between the nodes with more similar degrees if the current state is Case II or III. When decreasing the assortativity coefficient, Case III is chosen to set an edge between the nodes with the largest and smallest degrees if the current state is Case I or II. We increase or decrease the assortativity coefficient by repeating the edge rewiring in a greedy way and continue until the assortativity coefficient is no longer changed. The assortativity coefficient r monotonically increases or decreases with this method.

Bottom Line: The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree-degree correlations, is still unclear.Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity.Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.

View Article: PubMed Central - PubMed

Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

ABSTRACT
Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree-degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.

Show MeSH
Related in: MedlinePlus