Preferential behaviour and scaling in diffusive dynamics on networks

Self Cite

We study structure, eigenvalue spectra and random walk dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their internal structure as scale-free and correlated subgraphs, and the topology of connecting network. Within the exhaustive spectral analysis for both the adjacency matrix and the normalized Laplacian matrix we identify the spectral properties which characterize the mesoscopic structure of sparse cyclic graphs and trees. The minimally connected nodes, clustering, and the average connectivity affect the central part of the spectrum. The number of distinct modules leads to an extra peak at the lower part of the Laplacian spectrum in cyclic graphs. Such a peak does not occur in the case of topologically distinct tree-subgraphs connected on a tree. Whereas the associated eigenvectors remain localized on the subgraphs both in trees and cyclic graphs. We also find a characteristic pattern of periodic localization along the chains on the tree for the eigenvector components associated with the largest eigenvalue λ L = 2 of the Laplacian. Further differences between the cyclic modular graphs and trees are found by the statistics of random walks return times and hitting patterns at nodes on these graphs. The distribution of first return times averaged over all nodes exhibits a stretched exponential tail with the exponent σ ≈ 1/3 for trees and σ ≈ 2/3 for cyclic graphs, which is independent on their mesoscopic and global structure.

“…As shown in Fig. 10c, long-range correlations in the diffusion processes on networks lead to a non-universal scaling relation [25] …”

Section: Random Walks On Trees and Cyclic Modular Networkmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Spectral and dynamical properties in classes of sparse networks with mesoscopic inhomogeneities

Mitrović

Tadić

2009

Self Cite

“…In biological physics, the scaling relationship between the two quantities, also called Taylor's law, was originally discovered in the densities of different species of organisms [20], where the scaling exponent is a crucial quantity in characterizing or classifying the underlying dynamics of the system. In complex transportation systems such as rivers, highways, the Internet, and microchips, the scaling relationship between the nodal flux fluctuation σ and the mean flux f has also attracted much attention [13][14][15][16][17][18][19], with values of the scaling exponent typically in the range [0.5,1.0]. For human movements in cyberspace and physical space, we find the scaling relation between the two quantities as σ ∼ f β and that the scaling exponent β assumes a value greater than unity, hence the term superlinear scaling.…”

mentioning

confidence: 99%

Scaling and correlation of human movements in cyberspace and physical space

Zhao

Huang

et al. 2014

Understanding the dynamics of human movements is key to issues of significant current interest such as behavioral prediction, recommendation, and control of epidemic spreading. We collect and analyze big data sets of human movements in both cyberspace (through browsing of websites) and physical space (through mobile towers) and find a superlinear scaling relation between the mean frequency of visit f and its fluctuation σ : σ ∼ f β with β ≈ 1.2. The probability distribution of the visiting frequency is found to be a stretched exponential function. We develop a model incorporating two essential ingredients, preferential return and exploration, and show that these are necessary for generating the scaling relation extracted from real data. A striking finding is that human movements in cyberspace and physical space are strongly correlated, indicating a distinctive behavioral identifying characteristic and implying that the behaviors in one space can be used to predict those in the other. Traditionally, human movements are restricted to the real physical space (or geospace). Pioneering works demonstrated that there are intrinsic patterns underlying human mobility in physical space [1][2][3], which are key to deciphering the dynamics of human behaviors with wide applications ranging from traffic forecasting [4] to epidemic prevention [5]. Triggered by the tremendous advances in modern information and communication technologies, at present as well as in the future, human movements occur not only in physical space but also in virtual or cyberspace. Here movements in cyberspace are defined broadly as changes in online activities, typically corresponding to switchings in the websites of exploration. Examples of cyberspace movements include World Wide Web surfing along hyperlinks and continuous shopping from commercial websites in a single online session. Do human movements in cyberspace and physical space share common features? Are there general scaling relations underlying human movements in both spaces?Studies of human behaviors have been greatly facilitated by the ubiquity of massive empirical data sets (big data sets) that typically record individuals' movements on various temporal and spatial scales [6,7]. For example, great insights into the dynamics of human movements in physical space were gained by tracking and analyzing the dispersal of dollar bills [1] and through mobile phone [2] and GPS [8] data. There were also efforts to uncover human movements in cyberspace during web surfing [9][10][11] and to probe into human interests dynamics unfolded during cyberspace shopping and browsing [12].In this paper we analyze data sets that record mobile phone users' visits to websites in cyberspace and to mobile towers in the physical space simultaneously and search for a correlation between the movements and general scaling relations. Distinguished from existing approaches to humanmobility analysis [1-3], we focus on the relationship between * ying-cheng.lai@asu.edu flux and fluctuations [13][14][15][16][17][18][19]. In pa...

“…However, this strategy isn't optimal due to the time-dependant fluctuation of the number of packets passing through each link [34,35]. That is to say, the strategy C is very good as a static strategy while it fails to capture the real-time traffic in the network.…”

Section: Simulation Resultsmentioning

confidence: 99%

Efficient routing strategies in scale-free networks with limited bandwidth

Tang

Zhou

2011

We study the traffic dynamics in complex networks where each link is assigned a limited and identical bandwidth. Although the first-in-first-out (FIFO) queuing rule is widely applied in the routing protocol of information packets, here we argue that if we drop this rule, the overall throughput of the network can be remarkably enhanced. We proposed some efficient routing strategies that do not strictly obey the FIFO rule. Comparing with the routine shortest path strategy, the throughput for both Barabási-Albert (BA) networks and the real Internet, the throughput can be improved more than five times. We calculate the theoretical limitation of the throughput. In BA networks, our proposed strategy can achieve 88% of the theoretical optimum, yet for the real Internet, it is about 12%, implying that we have a huge space to further improve the routing strategy for the real Internet. Finally we discuss possibly promising ways to design more efficient routing strategies for the Internet.