Flow graphs: Interweaving dynamics and structure
Renaud Lambiotte,Renaud Lambiotte,Roberta Sinatra,Roberta Sinatra,Jean-Charles Delvenne,Tim S. Evans,Mauricio Barahona,Vito Latora,Vito Latora +8 more
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.Abstract:
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential because different dynamical processes may be affected very differently by network topology. A full characterization of such systems thus requires a formalization that encompasses both aspects simultaneously, rather than relying only on the topological adjacency matrix. To achieve this, we introduce the concept of flow graphs, namely weighted networks where dynamical flows are embedded into the link weights. Flow graphs provide an integrated representation of the structure and dynamics of the system, which can then be analyzed with standard tools from network theory. Conversely, a structural network feature of our choice can also be used as the basis for the construction of a flow graph that will then encompass a dynamics biased by such a feature. We illustrate the ideas by focusing on the mathematical properties of generic linear processes on complex networks that can be represented as biased random walks and their dual consensus dynamics, and show how our framework improves our understanding of these processes.read more
Citations
More filters
疟原虫var基因转换速率变化导致抗原变异[英]/Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A
TL;DR: PfPMP1)与感染红细胞、树突状组胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作�ly.
Journal ArticleDOI
Random walks and diffusion on networks
TL;DR: The theory and applications of random walks on networks are surveyed, restricting ourselves to simple cases of single and non-adaptive random walkers, and three main types are distinguished: discrete-time random walks, node-centric continuous-timerandom walks, and edge-centric Continuous-Time random walks.
Journal ArticleDOI
Random walks and diffusion on networks
TL;DR: Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures as discussed by the authors, and they are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can extract information about important entities or dense groups of entities in networks.
Journal ArticleDOI
Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks
TL;DR: In this paper, the Markov Stability, a time-parametrized function defined in terms of the statistical properties of a Markov process taking place on the graph, is introduced to find multi-scale community structure in large networks.
Journal ArticleDOI
Collective Phenomena Emerging from the Interactions between Dynamical Processes in Multiplex Networks
TL;DR: It is shown numerically, and it is proved analytically, that the multilayer coupling induces a spontaneous explosive synchronization and a heterogeneous distribution of allocations, otherwise not present in the two systems considered separately.
References
More filters
疟原虫var基因转换速率变化导致抗原变异[英]/Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A
TL;DR: PfPMP1)与感染红细胞、树突状组胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作�ly.
Book
Spectral Graph Theory
TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness
BookDOI
The structure and dynamics of networks
TL;DR: The degree distribution, twopoint correlations, and clustering are the studied topological properties and an evolution of networks is studied to shed light on the influence the dynamics has on the network topology.
DissertationDOI
Problems in Decentralized Decision making and Computation.
TL;DR: A scheme whereby a set of decision makers (processors) exchange and update tentative decisions which minimize a common cost function, given information they possess is considered; it is shown that they are guaranteed to converge to consensus.
Proceedings ArticleDOI
Predictive energy management of a power-split hybrid electric vehicle
TL;DR: Simulation results over multiple driving cycles indicate better fuel economy over conventional strategies can be achieved and the proposed algorithm is causal and has the potential for real-time implementation.