Reactive explorers to unravel network topology
arXiv:1811.12284 · doi:10.1140/epjb/e2019-90700-3
Abstract
A procedure is developed and tested to recover the distribution of connectivity of an a priori unknown network, by sampling the dynamics of an ensemble made of reactive walkers. The relative weight between reaction and relocation is gauged by a scalar control parameter, which can be adjusted at will. Different equilibria are attained by the system, following the externally imposed modulation, and reflecting the interplay between reaction and diffusion terms. The information gathered on the observation node is used to predict the stationary density as displayed by the system, via a direct implementation of the celebrated Heterogeneous Mean Field (HMF) approximation. This knowledge translates into a linear problem which can be solved to return the entries of the sought distribution. A variant of the model is then considered which consists in assuming a localized source where the reactive constituents are injected, at a rate that can be adjusted as a stepwise function of time. The linear problem obtained when operating in this setting allows one to recover a fair estimate of the underlying system size. Numerical experiments are carried so as to challenge the predictive ability of the theory.
References in corpus (18)
- Statistical mechanics of complex networks
- Critical phenomena in complex networks
- Weak pairwise correlations imply strongly correlated network states in a neural population
- Random walks and diffusion on networks
- Inferring Network Topology from Complex Dynamics
- Maximal-entropy random walks in complex networks with limited information
- Scaling Properties of Random Walks on Small-World Networks
- Diffusion in a crowded environment
- Theory of diffusion-influenced reactions in complex geometries
- Brain modularity controls the critical behavior of spontaneous activity
- Hopping in the crowd to unveil network topology
- Chaos and correlated avalanches in excitatory neural networks with synaptic plasticity
- Impact of network structure on a model of diffusion and competitive interaction
- Diffusion of tagged particles in a crowded medium
- Heterogeneous Mean Field for neural networks with short term plasticity
- Reactive random walkers on complex networks
- Neural networks with excitatory and inhibitory components: direct and inverse problems by a mean-field approach
- Random Walks on Complex Networks