Random Walks on Stochastic Temporal Networks

@article{Hoffmann2013RandomWO,
  title={Random Walks on Stochastic Temporal Networks},
  author={Till Hoffmann and Mason A. Porter and Renaud Lambiotte},
  journal={ArXiv},
  year={2013},
  volume={abs/1306.0715}
}
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a… 
Random walk centrality for temporal networks
TLDR
A centrality measure for temporal networks based on random walks under periodic boundary conditions that is called TempoRank, which is applied to human interaction networks and shows that although it is important for a node to be connected to another node with many random walkers at the right moment, this effect is negligible in practice when the time order of link activation is included.
Random walks in time-varying networks with memory.
TLDR
This work analyzes how an individual's memory affects random-walk process unfolding on the network when the timescales of the processes of the random walk and the network evolution are comparable and finds that anindividual's memory enhances the activity fluctuation and leads to the formation of small clusters of mutual contacts with high activity nodes.
Backtracking and Mixing Rate of Diffusion on Uncorrelated Temporal Networks
TLDR
It is shown that non-Poisson dynamics may significantly slow down diffusion due to backtracking, by a mechanism intrinsically different from the standard bus paradox and related temporal mechanisms.
Edge-attractor random walks on dynamic networks
TLDR
The edge-attractor RW model is introduced in which the network dynamics is biased towards graph configurations displaying higher degree for the vertex currently occupied by the walker, and the joint process describing the edgeattractorRW on a time-reversible dynamic network is time reversible.
Rock-paper-scissors dynamics from random walks on temporal multiplex networks
TLDR
The slowing-down effect due to the competition on a multiplex network with heterogeneous layers activity as the walker is likely to be trapped for a longer time either on a single layer, or on an oriented cycle is numerically shown.
Rock-Paper-Scissors Random Walks on Temporal Multilayer Networks
TLDR
The slowing-down effect due to the competition on a heterogeneous multilayer as the walker is likely to be trapped for a longer time either on a single layer, or on an oriented cycle.
Modern temporal network theory: a colloquium
TLDR
This colloquium reviews the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years, which includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more.
Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks.
TLDR
This work introduces a methodology that allows to analytically predict causality-driven changes of diffusion speed in non-Markovian temporal networks and shows that compared with the time-aggregated network, non- Markovian characteristics can lead to both a slow-down or speed-up of diffusion.
Higher-order aggregate networks in the analysis of temporal networks: path structures and centralities
TLDR
A novel framework for the study of path-based centralities in higher-order aggregate networks, a recently proposed generalization of the commonly used static representation of time-stamped data is introduced.
Modeling random walkers on growing random networks
...
...

References

SHOWING 1-10 OF 64 REFERENCES
Generalized Master Equations for Non-Poisson Dynamics on Networks
TLDR
The effects of non-Poisson inter-event statistics on the dynamics of edges are examined, and the concept of a generalized master equation is applied to the study of continuous-time random walks on networks.
Random walks on temporal networks.
TLDR
It is shown that the random walk exploration is slower on temporal networks than it is on the aggregate projected network, even when the time is properly rescaled, and a fundamental role is played by the temporal correlations between consecutive contacts present in the data.
Maps of random walks on complex networks reveal community structure
TLDR
An information theoretic approach is introduced that reveals community structure in weighted and directed networks of large-scale biological and social systems and reveals a directional pattern of citation from the applied fields to the basic sciences.
Multiscale analysis of spreading in a large communication network
TLDR
A multiscale analysis shows that for the spreading velocity, time-domain inhomogeneities are as important as the network topology, which indicates the need to take time- domain information into account when studying spreading dynamics.
Non-Conservative Diffusion and its Application to Social Network Analysis
TLDR
This work argues that unlike a random walk, many interesting social phenomena, such as the spread of information or disease on a social network, are fundamentally non-conservative, and gives a scalable approximate algorithm for computing the Alpha-Centrality in a massive graph.
Temporal Networks
Path lengths, correlations, and centrality in temporal networks
  • R. K. Pan, J. Saramäki
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2011
TLDR
Differences between static and temporal properties are further highlighted in studies of the temporal closeness centrality, and correlations and heterogeneities in the underlying event sequences affect temporal path lengths, increasing temporal distances in communication networks and decreasing them in the air transport network.
Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
TLDR
A generalized framework of network quality functions was developed that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices.
Flow graphs: interweaving dynamics and structure
TLDR
This work introduces the concept of flow graphs, namely weighted networks where dynamical flows are embedded into the link weights, and focuses on the mathematical properties of generic linear processes on complex networks that can be represented as biased random walks and their dual consensus dynamics.
Connectivity and inference problems for temporal networks
TLDR
This work defines and studies the class of inference problems, in which it seeks to reconstruct a partially specified time labeling of a network in a manner consistent with an observed history of information flow, and provides results on two types of problems for temporal networks.
...
...