Centrality scaling in large networks

Betweenness centrality lies at the core of both transport and structural vulnerability properties of complex networks, however, it is computationally costly, and its measurement for networks with millions of nodes is near impossible. By introducing a multiscale decomposition of shortest paths, we show that the contributions to betweenness coming from geodesics not longer than L obey a characteristic scaling vs L, which can be used to predict the distribution of the full centralities. The method is also illustrated on a real-world social network of 5.5*10^6 nodes and 2.7*10^7 links

Rydberg transition frequencies from the Local Density Approximation

A method is given that extracts accurate Rydberg excitations from LDA density functional calculations, despite the short-ranged potential. For the case of He and Ne, the asymptotic quantum defects predicted by LDA are in less than 5% error, yielding transition frequency errors of less than 0.1eV.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let

Detection of Complex Networks Modularity by Dynamical Clustering

Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort ${\cal O}(KN)$ on a generic graph with $N$ nodes and $K$ links.Comment: 5 pages, 2 figures. Version accepted for publication on PRE Rapid Communications: figures changed and text adde

Time-dependent Density Functional calculation of e-H scattering

Phase shifts for single-channel elastic electron-atom scattering are derived from time-dependent density functional theory. The H$^-$ ion is placed in a spherical box, its discrete spectrum found, and phase shifts deduced. Exact-exchange yields an excellent approximation to the ground-state Kohn-Sham potential, while the adiabatic local density approximation yields good singlet and triplet phase shifts.Comment: 5 pages, 4 figures, 1 tabl

A Method to Find Community Structures Based on Information Centrality

Community structures are an important feature of many social, biological and technological networks. Here we study a variation on the method for detecting such communities proposed by Girvan and Newman and based on the idea of using centrality measures to define the community boundaries (M. Girvan and M. E. J. Newman, Community structure in social and biological networks Proc. Natl. Acad. Sci. USA 99, 7821-7826 (2002)). We develop an algorithm of hierarchical clustering that consists in finding and removing iteratively the edge with the highest information centrality. We test the algorithm on computer generated and real-world networks whose community structure is already known or has been studied by means of other methods. We show that our algorithm, although it runs to completion in a time O(n^4), is very effective especially when the communities are very mixed and hardly detectable by the other methods.Comment: 13 pages, 13 figures. Final version accepted for publication in Physical Review

Stark ionization of atoms and molecules within density functional resonance theory

We show that the energetics and lifetimes of resonances of finite systems under an external electric field can be captured by Kohn-Sham density functional theory (DFT) within the formalism of uniform complex scaling. Properties of resonances are calculated self-consistently in terms of complex densities, potentials, and wave functions using adapted versions of the known algorithms from DFT. We illustrate this new formalism by calculating ionization rates using the complex-scaled local density approximation and exact exchange. We consider a variety of atoms (H, He, Li, and Be) as well as the H2 molecule. Extensions are briefly discussed

N-representability and stationarity in time-dependent density functional theory

To construct an N-representable time-dependent density-functional theory, a generalization to the time domain of the Levy-Lieb (LL) constrained search algorithm is required. That the action is only stationary in the Dirac-Frenkel variational principle eliminates the possibility of basing the search on the action itself. Instead, we use the norm of the partial functional derivative of the action in the Hilbert space of the wave functions in place of the energy of the LL search. The electron densities entering the formalism are $N$-representable, and the resulting universal action functional has a unique stationary point in the density at that corresponding to the solution of the Schr\"{o}dinger equation. The original Runge-Gross (RG) formulation is subsumed within the new formalism. Concerns in the literature about the meaning of the functional derivatives and the internal consistency of the RG formulation are allayed by clarifying the nature of the functional derivatives entering the formalism.Comment: 9 pages, 0 figures, Phys. Rev. A accepted. Introduction was expanded, subsections reorganized, appendix and new references adde

Quantifying the connectivity of a network: The network correlation function method

Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as social networks. Lately, it was found that many of these networks display some common topological features, such as high clustering, small average path length (small world networks) and a power-law degree distribution (scale free networks). The topological features of a network are commonly related to the network's functionality. However, the topology alone does not account for the nature of the interactions in the network and their strength. Here we introduce a method for evaluating the correlations between pairs of nodes in the network. These correlations depend both on the topology and on the functionality of the network. A network with high connectivity displays strong correlations between its interacting nodes and thus features small-world functionality. We quantify the correlations between all pairs of nodes in the network, and express them as matrix elements in the correlation matrix. From this information one can plot the correlation function for the network and to extract the correlation length. The connectivity of a network is then defined as the ratio between this correlation length and the average path length of the network. Using this method we distinguish between a topological small world and a functional small world, where the latter is characterized by long range correlations and high connectivity. Clearly, networks which share the same topology, may have different connectivities, based on the nature and strength of their interactions. The method is demonstrated on metabolic networks, but can be readily generalized to other types of networks.Comment: 10 figure

eBay users form stable groups of common interest

Market segmentation of an online auction site is studied by analyzing the users' bidding behavior. The distribution of user activity is investigated and a network of bidders connected by common interest in individual articles is constructed. The network's cluster structure corresponds to the main user groups according to common interest, exhibiting hierarchy and overlap. Key feature of the analysis is its independence of any similarity measure between the articles offered on eBay, as such a measure would only introduce bias in the analysis. Results are compared to null models based on random networks and clusters are validated and interpreted using the taxonomic classifications of eBay categories. We find clear-cut and coherent interest profiles for the bidders in each cluster. The interest profiles of bidder groups are compared to the classification of articles actually bought by these users during the time span 6-9 months after the initial grouping. The interest profiles discovered remain stable, indicating typical interest profiles in society. Our results show how network theory can be applied successfully to problems of market segmentation and sociological milieu studies with sparse, high dimensional data.Comment: Major revision of the manuscript. Methodological improvements and inclusion of analysis of temporal development of user interests. 19 pages, 12 figures, 5 table

Recommended care for young people (15-19 years) after suicide attempts in certain European countries

Abstract Data on recommended care for young people aged 15±19 years after attempted suicide from nine European research centres dur- ing the period 1989±1992 were ana- lysed in terms of gender, history of previous suicide attempt and meth- ods used. Altogether 438 suicide attempts made by 353 boys and 1,102 suicide attempts made by 941 girls were included. Analyses of the total data from all centres showed that young people with a history of previous suicide attempt and those using violent methods had signi®- cantly higher chance of being rec- ommended aftercare than ®rst-time attempters or those choosing self- poisoning. There were no signi®cant di erences of being recommended care between genders. Logistic re- gression analyses of the material were performed and the results were similar. Both having previous at- tempted suicide (odds ratio 2.0, 95% CI 1.53±2.61) and using ``hard'' methods (odds ratio 1.71, 95% CI 1.49±1.96) were signi®cantly associ- ated with increased possibility of being recommended aftercare. When individual centres were analysed, large disparities of recommended care after suicide attempts were found and there were no uniform criteria of recommending care for young suicide attempters in Europe. Key words Young people ± attempted suicide ± method ± recommended car