Bosiljka Tadic

Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations.

We study the microscopic time fluctuations of traffic load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates R the traffic is stationary and the load time series exhibits antipersistence due to the regulatory role of the superstructure associated with two hub nodes in the network. We discuss how the superstructure affects the functioning of the network at high traffic density and at the jamming threshold. The degree of correlations systematically decreases with increasing traffic density and eventually disappears when approaching a jamming density R(c). Already before jamming we observe qualitative changes in the global network-load distributions and the particle queuing times. These changes are related to the occurrence of temporary crises in which the network-load increases dramatically, and then slowly falls back to a value characterizing free flow.

TRANSPORT ON COMPLEX NETWORKS: FLOW, JAMMING AND OPTIMIZATION

Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper, we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density ...

Dynamics of directed graphs: the world-wide Web

We introduce and simulate a growth model of the world-wide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing selected nodes. Emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the Web. The growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links. We obtain quantitative agreement with the recent empirical data in the real Web for the distributions of in- and out-links and for the size of the connected component. In a fully grown network of N nodes, we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node. The distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior. By decreasing the control parameter – average fraction β of updated and added links per time step – towards βc(N)<10% the Web can resume a critical structure with no giant component in it. We find a different universality class when the updates of links are not allowed, i.e., for β≡0, corresponding to the network of science citations.

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

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, the 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 lambda(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 sigma approximately 1/3 for trees and sigma approximately 2/3 for cyclic graphs, which is independent of their mesoscopic and global structure.

Information super-diffusion on structured networks

We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an improved local search method. Numerical simulations are performed in the regime of stationary workloads away from the jamming transition. We find that graph topology determines the properties of diffusion in a universal way, which is reflected by power laws in the transit time and velocity distributions of packets. With the use of multifractal scaling analysis and arguments of non-extensive statistics we find evidence that these power-laws are compatible with super-diffusive traffic on large networks. We are able to quantify the role of network topology on overall transport efficiency. Further, we demonstrate the implications of improved transport rules and discuss the importance of matching (global) topology with (local) transport rules for the optimal function of networks. The presented model should be applicable to a wide range of phenomena ranging from Internet traffic to protein transport along the cytoskeleton in biological cells.

Bloggers behavior and emergent communities in Blog space

AbstractInteractions between users in cyberspace may lead to phenomena different from those observed in common social networks. Here we analyse large data sets about users and Blogs which they write and comment, mapped onto a bipartite graph. In such enlarged Blog space we trace user activity over time, which results in robust temporal patterns of user-Blog behavior and the emergence of communities. With the spectral methods applied to the projection on weighted user network we detect clusters of users related to their common interests and habits. Our results suggest that different mechanisms may play the role in the case of very popular Blogs. Our analysis makes a suitable basis for theoretical modeling of the evolution of cyber communities and for practical study of the data, in particular for an efficient search of interesting Blog clusters and further retrieval of their contents by text analysis.

PACKET TRANSPORT ON SCALE-FREE NETWORKS

We introduce a model of information packet transport on networks in which the packets are posted by a given rate and move in parallel according to a local search algorithm. By performing a number of simulations we investigate the major kinetic properties of the transport as a function of the network geometry, the packet input rate and the buffer size. We find long-range correlations in the power spectra of arriving packet density and the networks activity bursts. The packet transit time distribution shows a power-law dependence with average transit time increasing with network size. This implies dynamic queuing on the network, in which many interacting queues are mutually driven by temporally correlated packet streams.

Driving rate effects in avalanche-mediated first-order phase transitions

We study the driving-rate and temperature dependence of the power-law exponents that characterize the avalanche distribution in first-order phase transitions. Measurements of acoustic emission in structural transitions in Cu-Zn-Al and Cu-Al-Ni are presented. We show how the observed behavior emerges within a general framework of competing time scales of avalanche relaxation, driving rate, and thermal fluctuations. We confirm our findings by numerical simulations of a prototype model.

Nonuniversal Scaling Behavior of Barkhausen Noise.

We simulate Barkhausen avalanches on fractal clusters in a two-dimensional diluted Ising ferromagnet with an effective Gaussian random field. We vary the concentration of defect sites

Tunneling model of proton glasses

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