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Community structure and multi-modal oscillations in complex networks.

Dorrian H, Borresen J, Amos M - PLoS ONE (2013)

Bottom Line: Moreover, we show that such global oscillations may arise as a direct result of network topology.We apply the method in two specific domains (metabolic networks and metropolitan transport) demonstrating the robustness of our results when applied to real world systems.We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) our observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems.

View Article: PubMed Central - PubMed

Affiliation: School of Computing, Mathematics and Digital Technology, Manchester Metropolitan University, Manchester, United Kingdom.

ABSTRACT
In many types of network, the relationship between structure and function is of great significance. We are particularly interested in community structures, which arise in a wide variety of domains. We apply a simple oscillator model to networks with community structures and show that waves of regular oscillation are caused by synchronised clusters of nodes. Moreover, we show that such global oscillations may arise as a direct result of network topology. We also observe that additional modes of oscillation (as detected through frequency analysis) occur in networks with additional levels of topological hierarchy and that such modes may be directly related to network structure. We apply the method in two specific domains (metabolic networks and metropolitan transport) demonstrating the robustness of our results when applied to real world systems. We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) our observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems.

Show MeSH
Coupling strength bifurcations for order parameter  for networks of clustered random networks.Each network contains  clusters of 45 randomly connected nodes with approximately  connections in each cluster. Here the frequencies are normally distributed with . (A) 50 additional random connections over the whole network; (B) 100 additional connections; (C) 150 additional connections. Note: The oscillatory regions indicate the parameter regimes where oscillatory behaviour will be observed.
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pone-0075569-g005: Coupling strength bifurcations for order parameter for networks of clustered random networks.Each network contains clusters of 45 randomly connected nodes with approximately connections in each cluster. Here the frequencies are normally distributed with . (A) 50 additional random connections over the whole network; (B) 100 additional connections; (C) 150 additional connections. Note: The oscillatory regions indicate the parameter regimes where oscillatory behaviour will be observed.

Mentions: We first investigate the effect of varying coupling strength, , using standard bifurcation techniques. Figure 5 shows typical one parameter bifurcation diagrams of the global order parameter, , as is increased from an initial value of to . Here, the initial phases of the oscillators are drawn from a uniform distribution, . At each iteration of the simulation the value of is increased in small increments, typically of around and we show bifurcations using , and random additional connections (see Figure 5).


Community structure and multi-modal oscillations in complex networks.

Dorrian H, Borresen J, Amos M - PLoS ONE (2013)

Coupling strength bifurcations for order parameter  for networks of clustered random networks.Each network contains  clusters of 45 randomly connected nodes with approximately  connections in each cluster. Here the frequencies are normally distributed with . (A) 50 additional random connections over the whole network; (B) 100 additional connections; (C) 150 additional connections. Note: The oscillatory regions indicate the parameter regimes where oscillatory behaviour will be observed.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3794975&req=5

pone-0075569-g005: Coupling strength bifurcations for order parameter for networks of clustered random networks.Each network contains clusters of 45 randomly connected nodes with approximately connections in each cluster. Here the frequencies are normally distributed with . (A) 50 additional random connections over the whole network; (B) 100 additional connections; (C) 150 additional connections. Note: The oscillatory regions indicate the parameter regimes where oscillatory behaviour will be observed.
Mentions: We first investigate the effect of varying coupling strength, , using standard bifurcation techniques. Figure 5 shows typical one parameter bifurcation diagrams of the global order parameter, , as is increased from an initial value of to . Here, the initial phases of the oscillators are drawn from a uniform distribution, . At each iteration of the simulation the value of is increased in small increments, typically of around and we show bifurcations using , and random additional connections (see Figure 5).

Bottom Line: Moreover, we show that such global oscillations may arise as a direct result of network topology.We apply the method in two specific domains (metabolic networks and metropolitan transport) demonstrating the robustness of our results when applied to real world systems.We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) our observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems.

View Article: PubMed Central - PubMed

Affiliation: School of Computing, Mathematics and Digital Technology, Manchester Metropolitan University, Manchester, United Kingdom.

ABSTRACT
In many types of network, the relationship between structure and function is of great significance. We are particularly interested in community structures, which arise in a wide variety of domains. We apply a simple oscillator model to networks with community structures and show that waves of regular oscillation are caused by synchronised clusters of nodes. Moreover, we show that such global oscillations may arise as a direct result of network topology. We also observe that additional modes of oscillation (as detected through frequency analysis) occur in networks with additional levels of topological hierarchy and that such modes may be directly related to network structure. We apply the method in two specific domains (metabolic networks and metropolitan transport) demonstrating the robustness of our results when applied to real world systems. We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) our observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems.

Show MeSH