Reactive immunization on complex networks

Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel information across the network. On the other hand, static topological quantities measuring the connectivity structure are independent on the dynamical mechanisms of the infection. A natural question is therefore how to improve the topological analysis by some kind of dynamical information that may be extracted from the ongoing infection itself. In this spirit, we propose a novel vaccination scheme that exploits information from the details of the infection pattern at the moment when the vaccination strategy is applied. Numerical simulations of the infection process show that the proposed immunization strategy is effective and robust on a wide class of complex networks

Controlling edge dynamics in complex networks

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degrees enhance the controllability of the proposed dynamics.Comment: Preprint. 24 pages, 4 figures, 2 tables. Source code available at http://github.com/ntamas/netctr

Effect of correlations on network controllability

A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network characteristics on the minimal number of driver nodes required to control a network. We find that clustering and modularity have no discernible impact, but the symmetries of the underlying matching problem can produce linear, quadratic or no dependence on degree correlation coefficients, depending on the nature of the underlying correlations. The results are supported by numerical simulations and help narrow the observed gap between the predicted and the observed number of driver nodes in real networks

Multiple Scale-Free Structures in Complex Ad-Hoc Networks

This paper develops a framework for analyzing and designing dynamic networks comprising different classes of nodes that coexist and interact in one shared environment. We consider {\em ad hoc} (i.e., nodes can leave the network unannounced, and no node has any global knowledge about the class identities of other nodes) {\em preferentially grown networks}, where different classes of nodes are characterized by different sets of local parameters used in the stochastic dynamics that all nodes in the network execute. We show that multiple scale-free structures, one within each class of nodes, and with tunable power-law exponents (as determined by the sets of parameters characterizing each class) emerge naturally in our model. Moreover, the coexistence of the scale-free structures of the different classes of nodes can be captured by succinct phase diagrams, which show a rich set of structures, including stable regions where different classes coexist in heavy-tailed and light-tailed states, and sharp phase transitions. Finally, we show how the dynamics formulated in this paper will serve as an essential part of {\em ad-hoc networking protocols}, which can lead to the formation of robust and efficiently searchable networks (including, the well-known Peer-To-Peer (P2P) networks) even under very dynamic conditions

Highly intensive data dissemination in complex networks

This paper presents a study on data dissemination in unstructured Peer-to-Peer (P2P) network overlays. The absence of a structure in unstructured overlays eases the network management, at the cost of non-optimal mechanisms to spread messages in the network. Thus, dissemination schemes must be employed that allow covering a large portion of the network with a high probability (e.g.~gossip based approaches). We identify principal metrics, provide a theoretical model and perform the assessment evaluation using a high performance simulator that is based on a parallel and distributed architecture. A main point of this study is that our simulation model considers implementation technical details, such as the use of caching and Time To Live (TTL) in message dissemination, that are usually neglected in simulations, due to the additional overhead they cause. Outcomes confirm that these technical details have an important influence on the performance of dissemination schemes and that the studied schemes are quite effective to spread information in P2P overlay networks, whatever their topology. Moreover, the practical usage of such dissemination mechanisms requires a fine tuning of many parameters, the choice between different network topologies and the assessment of behaviors such as free riding. All this can be done only using efficient simulation tools to support both the network design phase and, in some cases, at runtime

Predicting link directions via a recursive subgraph-based ranking

Link directions are essential to the functionality of networks and their prediction is helpful towards a better knowledge of directed networks from incomplete real-world data. We study the problem of predicting the directions of some links by using the existence and directions of the rest of links. We propose a solution by first ranking nodes in a specific order and then predicting each link as stemming from a lower-ranked node towards a higher-ranked one. The proposed ranking method works recursively by utilizing local indicators on multiple scales, each corresponding to a subgraph extracted from the original network. Experiments on real networks show that the directions of a substantial fraction of links can be correctly recovered by our method, which outperforms either purely local or global methods.Comment: 6 pages, 5 figures; revised arguments for methods section; figures replotted; minor revision