Mapping from structure to dynamics: A unified view of dynamical processes on networks

Jie Zhang*, Changsong ZHOU, Xiaoke Xu, Michael Small

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

34 Citations (Scopus)


Although it is unambiguously agreed that structure plays a fundamental role in shaping the collective dynamics of complex systems, how structure determines dynamics exactly still remains unclear. We investigate a general computational transformation by which we can map the network topology directly to the dynamical patterns emergent on it-independent of the nature of the dynamical processes. Remarkably, we find that many seemingly different dynamical processes on networks, such as coupled oscillators, ensemble neuron firing, epidemic spreading and diffusion can all be understood and unified through this same procedure. Utilizing the inherent multiscale nature of this structure-dynamics transformation, we further define a multiscale complexity measure, which can quantify the functional diversity a general network can support at different organization levels using only its structure. We find that a wide variety of topological features observed in real networks, such as modularity, hierarchy, degree heterogeneity and mixing all result in higher complexity. This result suggests that the demand for functional diversity is driving the structural evolution of physical networks.

Original languageEnglish
Article number026116
JournalPhysical Review E
Issue number2
Publication statusPublished - 27 Aug 2010

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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