Detecting degree symmetries in networks

The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping degree sequences. These measures are evaluated on artificial and real networks. Specifically we consider vertices in the human metabolic network. We also measure the average degree-symmetry coefficient for different classes of real-world network. We find that most studied examples are weakly positively degree-symmetric. The exceptions are an airport network (having a negative degree-symmetry coefficient) and one-mode projections of social affiliation networks that are rather strongly degree-symmetric

Immunization of networks with community structure

In this study, an efficient method to immunize modular networks (i.e., networks with community structure) is proposed. The immunization of networks aims at fragmenting networks into small parts with a small number of removed nodes. Its applications include prevention of epidemic spreading, intentional attacks on networks, and conservation of ecosystems. Although preferential immunization of hubs is efficient, good immunization strategies for modular networks have not been established. On the basis of an immunization strategy based on the eigenvector centrality, we develop an analytical framework for immunizing modular networks. To this end, we quantify the contribution of each node to the connectivity in a coarse-grained network among modules. We verify the effectiveness of the proposed method by applying it to model and real networks with modular structure.Comment: 3 figures, 1 tabl

A Markov model for inferring flows in directed contact networks

Directed contact networks (DCNs) are a particularly flexible and convenient class of temporal networks, useful for modeling and analyzing the transfer of discrete quantities in communications, transportation, epidemiology, etc. Transfers modeled by contacts typically underlie flows that associate multiple contacts based on their spatiotemporal relationships. To infer these flows, we introduce a simple inhomogeneous Markov model associated to a DCN and show how it can be effectively used for data reduction and anomaly detection through an example of kernel-level information transfers within a computer.Comment: 12 page

Reconstructing Holocene geomagnetic field variation: new methods, models and implications

Reconstructions of the Holocene geomagnetic field and how it varies on millennial timescales are important for understanding processes in the core but may also be used to study long-term solar-terrestrial relationships and as relative dating tools for geological and archaeological archives. Here, we present a new family of spherical harmonic geomagnetic field models spanning the past 9000 yr based on magnetic field directions and intensity stored in archaeological artefacts, igneous rocks and sediment records. A new modelling strategy introduces alternative data treatments with a focus on extracting more information from sedimentary data. To reduce the influence of a few individual records all sedimentary data are resampled in 50-yr bins, which also means that more weight is given to archaeomagnetic data during the inversion. The sedimentary declination data are treated as relative values and adjusted iteratively based on prior information. Finally, an alternative way of treating the sediment data chronologies has enabled us to both assess the likely range of age uncertainties, often up to and possibly exceeding 500 yr and adjust the timescale of each record based on comparisons with predictions from a preliminary model. As a result of the data adjustments, power has been shifted from quadrupole and octupole to higher degrees compared with previous Holocene geomagnetic field models. We find evidence for dominantly westward drift of northern high latitude high intensity flux patches at the core mantle boundary for the last 4000 yr. The new models also show intermittent occurrence of reversed flux at the edge of or inside the inner core tangent cylinder, possibly originating from the equator

Handling oversampling in dynamic networks using link prediction

Oversampling is a common characteristic of data representing dynamic networks. It introduces noise into representations of dynamic networks, but there has been little work so far to compensate for it. Oversampling can affect the quality of many important algorithmic problems on dynamic networks, including link prediction. Link prediction seeks to predict edges that will be added to the network given previous snapshots. We show that not only does oversampling affect the quality of link prediction, but that we can use link prediction to recover from the effects of oversampling. We also introduce a novel generative model of noise in dynamic networks that represents oversampling. We demonstrate the results of our approach on both synthetic and real-world data.Comment: ECML/PKDD 201

Sampling of temporal networks: methods and biases

Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example, human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is that they are sampled within temporal and spatial frames. Furthermore, one might wish to subsample networks to reduce their size for better visualization or to perform computationally intensive simulations. The sampling method may affect the network structure and thus caution is necessary to generalize results based on samples. In this paper, we study four sampling strategies applied to a variety of real-life temporal networks. We quantify the biases generated by each sampling strategy on a number of relevant statistics such as link activity, temporal paths and epidemic spread. We find that some biases are common in a variety of networks and statistics, but one strategy, uniform sampling of nodes, shows improved performance in most scenarios. Given the particularities of temporal network data and the variety of network structures, we recommend that the choice of sampling methods be problem oriented to minimize the potential biases for the specific research questions on hand. Our results help researchers to better design network data collection protocols and to understand the limitations of sampled temporal network data

Zero Temperature Glass Transition in the Two-Dimensional Gauge Glass Model

We investigate dynamic scaling properties of the two-dimensional gauge glass model for the vortex glass phase in superconductors with quenched disorder. From extensive Monte Carlo simulations we obtain static and dynamic finite size scaling behavior, where the static simulations use a temperature exchange method to ensure convergence at low temperatures. Both static and dynamic scaling of Monte Carlo data is consistent with a glass transition at zero temperature. We study a dynamic correlation function for the superconducting order parameter, as well as the phase slip resistance. From the scaling of these two functions, we find evidence for two distinct diverging correlation times at the zero temperature glass transition. The longer of these time scales is associated with phase slip fluctuations across the system that lead to finite resistance at any finite temperature, while the shorter time scale is associated with local phase fluctuations.Comment: 8 pages, 10 figures; v2: some minor correction