Link Prediction with Social Vector Clocks

State-of-the-art link prediction utilizes combinations of complex features derived from network panel data. We here show that computationally less expensive features can achieve the same performance in the common scenario in which the data is available as a sequence of interactions. Our features are based on social vector clocks, an adaptation of the vector-clock concept introduced in distributed computing to social interaction networks. In fact, our experiments suggest that by taking into account the order and spacing of interactions, social vector clocks exploit different aspects of link formation so that their combination with previous approaches yields the most accurate predictor to date.Comment: 9 pages, 6 figure

Weighted network modules

The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with weights) for weighted networks based on the concept of percolating k-cliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted k-clique percolation on (weighted) Erdos-Renyi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute three-link weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomised control graphs as well, we show that groups of 3 or more strong links prefer to cluster together in both original graphs.Comment: 19 pages, 7 figure

Efficiency of informational transfer in regular and complex networks

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study non-clustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small-worlds that includes {\it declustered} networks, and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.Comment: 10 pages and 9 figure

Search in Complex Networks : a New Method of Naming

We suggest a method for routing when the source does not posses full information about the shortest path to the destination. The method is particularly useful for scale-free networks, and exploits its unique characteristics. By assigning new (short) names to nodes (aka labelling) we are able to reduce significantly the memory requirement at the routers, yet we succeed in routing with high probability through paths very close in distance to the shortest ones.Comment: 5 pages, 4 figure

Statistical and Dynamical Study of Disease Propagation in a Small World Network

We study numerically statistical properties and dynamical disease propagation using a percolation model on a one dimensional small world network. The parameters chosen correspond to a realistic network of school age children. We found that percolation threshold decreases as a power law as the short cut fluctuations increase. We found also the number of infected sites grows exponentially with time and its rate depends logarithmically on the density of susceptibles. This behavior provides an interesting way to estimate the serology for a given population from the measurement of the disease growing rate during an epidemic phase. We have also examined the case in which the infection probability of nearest neighbors is different from that of short cuts. We found a double diffusion behavior with a slower diffusion between the characteristic times.Comment: 12 pages LaTex, 10 eps figures, Phys.Rev.E Vol. 64, 056115 (2001

Citation Networks in High Energy Physics

The citation network constituted by the SPIRES data base is investigated empirically. The probability that a given paper in the SPIRES data base has $k$ citations is well described by simple power laws, $P(k) \propto k^{-\alpha}$, with $\alpha \approx 1.2$ for $k$ less than 50 citations and $\alpha \approx 2.3$ for 50 or more citations. Two models are presented that both represent the data well, one which generates power laws and one which generates a stretched exponential. It is not possible to discriminate between these models on the present empirical basis. A consideration of citation distribution by subfield shows that the citation patterns of high energy physics form a remarkably homogeneous network. Further, we utilize the knowledge of the citation distributions to demonstrate the extreme improbability that the citation records of selected individuals and institutions have been obtained by a random draw on the resulting distribution.Comment: 9 pages, 6 figures, 2 table

Response Functions to Critical Shocks in Social Sciences: An Empirical and Numerical Study

We show that, provided one focuses on properly selected episodes, one can apply to the social sciences the same observational strategy that has proved successful in natural sciences such as astrophysics or geodynamics. For instance, in order to probe the cohesion of a policy, one can, in different countries, study the reactions to some huge and sudden exogenous shocks, which we call Dirac shocks. This approach naturally leads to the notion of structural (as opposed or complementary to temporal) forecast. Although structural predictions are by far the most common way to test theories in the natural sciences, they have been much less used in the social sciences. The Dirac shock approach opens the way to testing structural predictions in the social sciences. The examples reported here suggest that critical events are able to reveal pre-existing ``cracks'' because they probe the social cohesion which is an indicator and predictor of future evolution of the system, and in some cases foreshadows a bifurcation. We complement our empirical work with numerical simulations of the response function (``damage spreading'') to Dirac shocks in the Sznajd model of consensus build-up. We quantify the slow relaxation of the difference between perturbed and unperturbed systems, the conditions under which the consensus is modified by the shock and the large variability from one realization to another

Multifractal analysis of complex networks

Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions $D_{q}$ of some theoretical networks, namely scale-free networks, small world networks and random networks, and one kind of real networks, namely protein-protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein-protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of $D_{q}$ due to changes in the parameters of the theoretical network models is also discussed.Comment: 18 pages, 7 figures, 4 table

Agreement on the perception of moral character

This study tested for inter-judge agreement on moral character. A sample of students and community members rated their own moral character using a measure that tapped six moral character traits. Friends, family members, and/or acquaintances rated these targets on the same traits. Self/other and inter-informant agreement was found at the trait level for both a general character factor and for residual variance explained by individual moral character traits, as well as at the individual level (judges agreed on targets’ “moral character profiles”). Observed inter-judge agreement constitutes evidence for the existence of moral character, and raises questions about the nature of moral character traits

Evolution equations of curvature tensors along the hyperbolic geometric flow

We consider the hyperbolic geometric flow $\frac{\partial^2}{\partial t^2}g(t)=-2Ric_{g(t)}$ introduced by Kong and Liu [KL]. When the Riemannian metric evolve, then so does its curvature. Using the techniques and ideas of S.Brendle [Br,BS], we derive evolution equations for the Levi-Civita connection and the curvature tensors along the hyperbolic geometric flow. The method and results are computed and written in global tensor form, different from the local normal coordinate method in [DKL1]. In addition, we further show that any solution to the hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.Comment: 15 page