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

Network reachability of real-world contact sequences

We use real-world contact sequences, time-ordered lists of contacts from one person to another, to study how fast information or disease can spread across network of contacts. Specifically we measure the reachability time -- the average shortest time for a series of contacts to spread information between a reachable pair of vertices (a pair where a chain of contacts exists leading from one person to the other) -- and the reachability ratio -- the fraction of reachable vertex pairs. These measures are studied using conditional uniform graph tests. We conclude, among other things, that the network reachability depends much on a core where the path lengths are short and communication frequent, that clustering of the contacts of an edge in time tend to decrease the reachability, and that the order of the contacts really do make sense for dynamical spreading processes.Comment: (v2: fig. 1 fixed

Exploring the assortativity-clustering space of a network's degree sequence

Nowadays there is a multitude of measures designed to capture different aspects of network structure. To be able to say if the structure of certain network is expected or not, one needs a reference model (null model). One frequently used null model is the ensemble of graphs with the same set of degrees as the original network. In this paper we argue that this ensemble can be more than just a null model -- it also carries information about the original network and factors that affect its evolution. By mapping out this ensemble in the space of some low-level network structure -- in our case those measured by the assortativity and clustering coefficients -- one can for example study how close to the valid region of the parameter space the observed networks are. Such analysis suggests which quantities are actively optimized during the evolution of the network. We use four very different biological networks to exemplify our method. Among other things, we find that high clustering might be a force in the evolution of protein interaction networks. We also find that all four networks are conspicuously robust to both random errors and targeted attacks

Nonlocal evolution of weighted scale-free networks

We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the network is determined nonlocally, this approach can explain the generic nonlinear scaling between the strength and the degree of a node. We demonstrate by a simple model that the strength-driven evolution scheme recently introduced can be generalized to a nonlinear preferential attachment rule, generating the power-law behaviors in degree and in strength simultaneously.Comment: 4 pages, 4 figures, final version published in PR

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

Effect of transformation by Rous sarcoma virus on the character and distribution of actin in Rat-1 fibroblasts: a biochemical and microscopical study.

Actin has been measured in subcellular fractions from Rat-1 fibroblasts and in Rous sarcoma virus-transformed Rat-1 cells (VIT), using the DNase 1 inhibition assay. The transformed cells showed a significant shift in the actin monomer (G)in equilibrium with polymer (F) equilibrium within the cell cytosol, and a significant increase in actin in the Triton-insoluble cytoskeletal core in comparison with untransformed cells. This incorporation of actin into the cytoskeletal core fraction is associated with a change in filamentous actin assemblies from 'stress fibre' patterns to punctate filament aggregates. These differences have been correlated with changes in morphology, in actin, vinculin and alpha-actinin distribution, in adhesion plaque formation and with the production of pp60v-src-associated protein kinase activity in the transformed cells. Changes in actin distribution and its polymerization in response to src-gene expression may play an important role in the determination of the transformed cell characteristics