Diffusion on networked systems is a question of time or structure

Abstract

Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the strong assumption that networks are static entities where temporal aspects can be neglected. Here we propose a generalised formalism for linear dynamics on complex networks, able to incorporate statistical properties of the timings at which events occur. We show that the diffusion dynamics is affected by the network community structure and by the temporal properties of waiting times between events. We identify the main mechanism --- network structure, burstiness or fat-tails of waiting times --- determining the relaxation times of stochastic processes on temporal networks, in the absence of temporal-structure correlations. We identify situations when fine-scale structure can be discarded from the description of the dynamics or, conversely, when a fully detailed model is required due to temporal heterogeneities.

Fundamental revision from v1

References in corpus (20)

• Maps of random walks on complex networks reveal community structure
• Statistical Mechanics of Community Detection
• What's in a crowd? Analysis of face-to-face behavioral networks
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Estimating Potential Infection Transmission Routes in Hospital Wards Using Wearable Proximity Sensors
• A Poissonian explanation for heavy-tails in e-mail communication
• Robustness of community structure in networks
• Causality-Driven Slow-Down and Speed-Up of Diffusion in Non-Markovian Temporal Networks
• Information dynamics shape the networks of Internet-mediated prostitution
• Structure and Time-Evolution of an Internet Dating Community
• Random walks and search in time-varying networks
• Temporal Heterogeneities Increase the Prevalence of Epidemics on Evolving Networks
• Spreading Dynamics Following Bursty Human Activity Patterns
• Spectral methods for the detection of network community structure: a comparative analysis
• Spectral Coarse Graining and Synchronization in Oscillator Networks
• Birth and death of links control disease spreading in empirical contact networks
• Steady state and mean recurrence time for random walks on stochastic temporal networks
• Communication dynamics in finite capacity social networks
• Spreading dynamics on networks: the role of burstiness, topology and non-stationarity
• Turing Instability in Reaction-Diffusion Systems with a Single Diffuser: Characterization Based on Root Locus

Cited by in corpus (54)

• Random walks and diffusion on networks
• Modern temporal network theory: A colloquium
• The Statistical Physics of Real-World Networks
• Ranking in evolving complex networks
• Bursty Human Dynamics
• The effects of network structure, competition and memory time on social spreading phenomena
• The theory of Turing patterns on time varying networks
• Measuring burstiness for finite event sequences
• Randomized reference models for temporal networks
• Modeling the spread of fake news on Twitter
• Magnetic eigenmaps for community detection in directed networks
• Multiscale dynamical embeddings of complex networks
• Using higher-order Markov models to reveal flow-based communities in networks
• Does the brain behave like a (complex) network? I. Dynamics
• Individual-based approach to epidemic processes on arbitrary dynamic contact networks
• Sampling of Temporal Networks: Methods and Biases
• Dynamics on networks: competition of temporal and topological correlations
• Laplacian paths in complex networks: information core emerges from entropic transitions
• Contact-based model for epidemic spreading on temporal networks
• Exploring Temporal Networks with Greedy Walks
• Network Modularity Controls the Speed of Information Diffusion
• Impact of temporal network structures on the speed of consensus formation in opinion dynamics
• Correlated bursts in temporal networks slow down spreading
• Dynamic topologies of activity-driven temporal networks with memory
• Physically-interpretable classification of biological network dynamics for complex collective motions
• Random walk on temporal networks with lasting edges
• Modeling correlated bursts by the bursty-get-burstier mechanism
• Copula-based algorithm for generating bursty time series
• Burstiness and fractional diffusion on complex networks
• Directed Percolation in Random Temporal Network Models with Heterogeneities
• Hierarchical burst model for complex bursty dynamics
• Risk of coinfection outbreaks in temporal networks: a case study of a hospital contact network
• Burst-tree decomposition of time series reveals the structure of temporal correlations
• Analytically solvable autocorrelation function for weakly correlated interevent times
• Navigating temporal networks
• Limits of memory coefficient in measuring correlated bursts
• Empirical study of the role of the topology in spreading on communication networks
• Concurrency and reachability in tree-like temporal networks
• Higher-order temporal network effects through triplet evolution
• Entrograms and coarse graining of dynamics on complex networks
• Structured networks and coarse-grained descriptions: a dynamical perspective
• Multiple structural transitions in interacting networks
• Analysis of the competition among viral strains using a temporal interaction-driven contagion model
• The Waiting-Time Distribution for Network Partitions in Cascading Failures in Power Networks
• Structural and temporal heterogeneities on networks
• Copula-based analysis of the autocorrelation function for simple temporal networks
• Functional brain networks: great expectations, hard times, and the big leap forward
• Diffusion and synchronization dynamics reveal the multi-scale patterns of spatial segregation
• weg2vec: Event embedding for temporal networks
• ABM of osteoblast's mechanotransduction pathway: time patterns of critical events
• Memory-cognizant generalization to Simon's random-copying neutral model
• Correlations of network trajectories
• Characterizing the neural correlates of reasoning
• Rock-Paper-Scissors Random Walks on Temporal Multilayer Networks