Rewiring hierarchical scale-free networks: Influence on synchronizability and topology
arXiv:1707.04057 · doi:10.1209/0295-5075/119/30002
Abstract
Many real-world complex networks simultaneously exhibit topological features of scale-free behaviour and hierarchical organization. In this regard, deterministic scale-free [A.-L. Barabási \etal, Physica A, 299, 3 (2001)] and pseudofractal scale-free [S. N. Dorogovtsev \etal, Phy. Rev. E, 65, 6 (2002)] networks constitute notable models which simultaneously incorporate the aforementioned properties. The rules governing the formation of such networks are completely deterministic. However, real-world networks are presumably neither completely deterministic, nor perfectly hierarchical. Therefore, we suggest here perfectly hierarchical scale-free networks with randomly rewired edges as better representatives of practical networked systems. In particular, we preserve the scale-free degree distribution of the various deterministic networks but successively relax the hierarchical structure while rewiring them. We utilize the framework of master stability function in investigating the synchronizability of dynamical systems coupled on such rewired networks. Interestingly, this reveals that the process of rewiring is capable of significantly enhancing, as well as, deteriorating the synchronizability of the resulting networks. We investigate the influence of rewiring edges on the topological properties of the rewired networks and, in turn, their relation to the synchronizability of the respective topologies. Finally, we compare the synchronizability of deterministic scale-free and pseudofractcal scale-free networks with that of random scale-free networks (generated using the classical Barabási-Albert model of growth and preferential attachment) and find that the latter ones promote synchronizability better than their deterministic counterparts.
arXiv comment7 pages, 5 figures
References in corpus (34)
- Emergence of scaling in random networks
- Lethality and centrality in protein networks
- Hierarchical organization of modularity in metabolic networks
- The large-scale organization of metabolic networks
- Synchronization in complex networks
- Hierarchical structure and the prediction of missing links in networks
- Hierarchical Organization in Complex Networks
- Synchronization in small-world systems
- The Web of Human Sexual Contacts
- Topology of evolving networks: local events and universality
- Synchronization reveals topological scales in complex networks
- Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
- Detect overlapping and hierarchical community structure in networks
- Fast Response and Temporal Coding on Coherent Oscillations in Small-World Networks
- Network Synchronization, Diffusion, and the Paradox of Heterogeneity
- Pseudofractal Scale-free Web
- Deterministic Scale-Free Networks
- Synchronization on small-world networks
- Entangled networks, synchronization, and optimal network topology
- Enhancing complex-network synchronization
- Spectral Properties and Synchronization in Coupled Map Lattices
- Synchronization is optimal in non-diagonalizable networks
- Factors that predict better synchronizability on complex networks
- Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions
- Maximum Performance at Minimum Cost in Network Synchronization
- Multi-node basin stability in complex dynamical networks
- Coherence in scale-free networks of chaotic maps
- Hierarchical Synchrony of Phase Oscillators in Modular Networks
- Efficient Rewirings for Enhancing Synchronizability of Dynamical Networks
- Bounding network spectra for network design
- Optimization of synchronizability in multiplex networks
- Tweaking Synchronisation by Link Addition
- Recovery time after localized perturbations in complex dynamical networks
- Dynamical behaviours in time-delay systems with delayed feedback and digitized coupling