Dynamics on Spatial Networks and the Effect of Distance Coarse Graining

Very recently, a kind of spatial network constructed with power-law distance distribution and total energy constriction is proposed. Moreover, it has been pointed out that such spatial networks have the optimal exponents $\delta$ in the power-law distance distribution for the average shortest path, traffic dynamics and navigation. Because the distance is estimated approximately in real world, we present an distance coarse graining procedure to generate the binary spatial networks in this paper. We find that the distance coarse graining procedure will result in the shifting of the optimal exponents $\delta$. Interestingly, when the network is large enough, the effect of distance coarse graining can be ignored eventually. Additionally, we also study some main dynamic processes including traffic dynamics, navigation, synchronization and percolation on this spatial networks with coarse grained distance. The results lead us to the enhancement of spatial networks' specifical functions.Comment: 6 pages,6 figure

Synchronization in small-world systems

We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of the Laplacian of the graph. We show numerically that the addition of random shortcuts produces improved network synchronizability. Further, we use a perturbation analysis to place the synchronization threshold in relation to the boundaries of the small-world region. Our results also show that small-worlds synchronize as efficiently as random graphs and hypercubes, and more so than standard constructive graphs

Link Prediction in Complex Networks: A Survey

Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving mechanisms, and so on. This article summaries recent progress about link prediction algorithms, emphasizing on the contributions from physical perspectives and approaches, such as the random-walk-based methods and the maximum likelihood methods. We also introduce three typical applications: reconstruction of networks, evaluation of network evolving mechanism and classification of partially labelled networks. Finally, we introduce some applications and outline future challenges of link prediction algorithms.Comment: 44 pages, 5 figure

Missing and spurious interactions and the reconstruction of complex networks

Network analysis is currently used in a myriad of contexts: from identifying potential drug targets to predicting the spread of epidemics and designing vaccination strategies, and from finding friends to uncovering criminal activity. Despite the promise of the network approach, the reliability of network data is a source of great concern in all fields where complex networks are studied. Here, we present a general mathematical and computational framework to deal with the problem of data reliability in complex networks. In particular, we are able to reliably identify both missing and spurious interactions in noisy network observations. Remarkably, our approach also enables us to obtain, from those noisy observations, network reconstructions that yield estimates of the true network properties that are more accurate than those provided by the observations themselves. Our approach has the potential to guide experiments, to better characterize network data sets, and to drive new discoveries

Voter model on a directed network: Role of bidirectional opinion exchanges

The voter model with the node update rule is numerically investigated on a directed network. We start from a directed hierarchical tree, and split and rewire each incoming arc at the probability $p$. In order to discriminate the better and worse opinions, we break the $Z_2$ symmetry ($\sigma = \pm 1$) by giving a little more preference to the opinion $\sigma = 1$. It is found that as $p$ becomes larger, introducing more complicated pattern of information flow channels, and as the network size $N$ becomes larger, the system eventually evolves to the state in which more voters agree on the better opinion, even though the voter at the top of the hierarchy keeps the worse opinion. We also find that the pure hierarchical tree makes opinion agreement very fast, while the final absorbing state can easily be influenced by voters at the higher ranks. On the other hand, although the ordering occurs much slower, the existence of complicated pattern of bidirectional information flow allows the system to agree on the better opinion.Comment: 5 pages, 3 figures, Phys. Rev. E (in press

Edge modification criteria for enhancing the communicability of digraphs

We introduce new broadcast and receive communicability indices that can be used as global measures of how effectively information is spread in a directed network. Furthermore, we describe fast and effective criteria for the selection of edges to be added to (or deleted from) a given directed network so as to enhance these network communicability measures. Numerical experiments illustrate the effectiveness of the proposed techniques.Comment: 26 pages, 11 figures, 4 table