Supremacy distribution in evolving networks

We study a supremacy distribution in evolving Barabasi-Albert networks. The supremacy $s_i$ of a node $i$ is defined as a total number of all nodes that are younger than $i$ and can be connected to it by a directed path. For a network with a characteristic parameter $m=1,2,3,...$ the supremacy of an individual node increases with the network age as $t^{(1+m)/2}$ in an appropriate scaling region. It follows that there is a relation $s(k) \sim k^{m+1}$ between a node degree $k$ and its supremacy $s$ and the supremacy distribution $P(s)$ scales as $s^{-1-2/(1+m)}$. Analytic calculations basing on a continuum theory of supremacy evolution and on a corresponding rate equation have been confirmed by numerical simulations.Comment: 4 pages, 4 figure

Interplay between network structure and self-organized criticality

We investigate, by numerical simulations, how the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model can induce emergence of scale-free (SF) networks and how this emerging structure affects dynamics of the system. We also discuss how the observed phenomenon can be used to explain evolution of scientific collaboration.Comment: 4 pages, 4 figure

Thermodynamic forces, flows, and Onsager coefficients in complex networks

We present Onsager formalism applied to random networks with arbitrary degree distribution. Using the well-known methods of non-equilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a result of single node degree perturbation. The forces and the flows can be understood as a response of the system to events, such as random removal of nodes or intentional attacks on them. Finally, we show that cross effects (such as thermodiffusion, or thermoelectric phenomena), in which one force may not only give rise to its own corresponding flow, but to many other flows, can be observed also in complex networks.Comment: 4 pages, 2 figure

Universal scaling of distances in complex networks

Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k_i and k_j equals to =A-B log(k_i k_j). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree _nn calculated for the nearest neighbors and on network clustering coefficients.Comment: 4 pages, 3 figures, 1 tabl

Delivery Practices of Traditional Birth Attendants in Dhaka Slums, Bangladesh

This paper describes associations among delivery-location, training of birth attendants, birthing practices, and early postpartum morbidity in women in slum areas of Dhaka, Bangladesh. During November 1993–May 1995, data on delivery-location, training of birth attendants, birthing practices, delivery-related complications, and postpartum morbidity were collected through interviews with 1,506 women, 489 home-based birth attendants, and audits in 20 facilities where the women from this study gave birth. Associations among maternal characteristics, birth practices, delivery-location, and early postpartum morbidity were specifically explored. Self-reported postpartum morbidity was associated with maternal characteristics, delivery-related complications, and some birthing practices. Dais with more experience were more likely to use potentially-harmful birthing practices which increased the risk of postpartum morbidity among women with births at home. Postpartum morbidity did not differ by birth-location. Safe motherhood programmes must develop effective strategies to discourage potentially-harmful home-based delivery practices demonstrated to contribute to morbidity

Average path length in random networks

Analytic solution for the average path length in a large class of random graphs is found. We apply the approach to classical random graphs of Erd\"{o}s and R\'{e}nyi (ER) and to scale-free networks of Barab\'{a}si and Albert (BA). In both cases our results confirm previous observations: small world behavior in classical random graphs $l_{ER} \sim \ln N$ and ultra small world effect characterizing scale-free BA networks $l_{BA} \sim \ln N/\ln\ln N$. In the case of scale-free random graphs with power law degree distributions we observed the saturation of the average path length in the limit of $N\to\infty$ for systems with the scaling exponent $2< \alpha <3$ and the small-world behaviour for systems with $\alpha>3$.Comment: 4 pages, 2 figures, changed conten

Delivery Practices of Traditional Birth Attendants in Dhaka Slums, Bangladesh

This paper describes associations among delivery-location, training of birth attendants, birthing practices, and early postpartum morbidity in women in slum areas of Dhaka, Bangladesh. During November 1993-May 1995, data on delivery-location, training of birth attendants, birthing practices, delivery-related complications, and postpartum morbidity were collected through interviews with 1,506 women, 489 home-based birth attendants, and audits in 20 facilities where the women from this study gave birth. Associations among maternal characteristics, birth practices, delivery-location, and early postpartum morbidity were specifically explored. Self-reported postpartum morbidity was associated with maternal characteristics, delivery-related complications, and some birthing practices. Dais with more experience were more likely to use potentially-harmful birthing practices which increased the risk of postpartum morbidity among women with births at home. Postpartum morbidity did not differ by birth-location. Safe motherhood programmes must develop effective strategies to discourage potentially-harmful home-based delivery practices demonstrated to contribute to morbidity

Self-organized network evolution coupled to extremal dynamics

The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the dynamics of the Bak-Sneppen evolution model with the rules of the so-called fitness network model for establishing the topology of a network; each vertex is assigned a fitness, and the vertex with minimum fitness and its neighbours are updated in each iteration. At the same time, the links between the updated vertices and all other vertices are drawn anew with a fitness-dependent connection probability. We show analytically and numerically that the system self-organizes to a non-trivial state that differs from what is obtained when the two processes are decoupled. A power-law decay of dynamical and topological quantities above a threshold emerges spontaneously, as well as a feedback between different dynamical regimes and the underlying correlation and percolation properties of the network.Comment: Accepted version. Supplementary information at http://www.nature.com/nphys/journal/v3/n11/suppinfo/nphys729_S1.htm

Evolutionary Events in a Mathematical Sciences Research Collaboration Network

This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this study traces the evolution of the "here and now" using fixed-duration sliding windows. The analysis uses a suite of common network diagnostics, including the distributions of degrees, distances, and clustering, to track network structure. Several random models that call these diagnostics as parameters help tease them apart as factors from the values of others. Some behaviors are consistent over the entire interval, but most diagnostics indicate that the network's structural evolution is dominated by occasional dramatic shifts in otherwise steady trends. These behaviors are not distributed evenly across the network; stark differences in evolution can be observed between two major subnetworks, loosely thought of as "pure" and "applied", which approximately partition the aggregate. The paper characterizes two major events along the mathematics network trajectory and discusses possible explanatory factors.Comment: 30 pages, 14 figures, 1 table; supporting information: 5 pages, 5 figures; published in Scientometric

A Statistical Test of Heterogeneous Subgraph Densities to Assess Clusterability

Determining if a graph displays a clustered structure prior to subjecting it to any cluster detection technique has recently gained attention in the literature. Attempts to group graph vertices into clusters when a graph does not have a clustered structure is not only a waste of time; it will also lead to misleading conclusions. To address this problem, we introduce a novel statistical test, the-test, which is based on comparisons of local and global densities. Our goal is to assess whether a given graph meets the necessary conditions to be meaningfully summarized by clusters of vertices. We empirically explore our test’s behavior under a number of graph structures. We also compare it to other recently published tests. From a theoretical standpoint, our test is more general, versatile and transparent than recently published competing techniques. It is based on the examination of intuitive quantities, applies equally to weighted and unweighted graphs and allows comparisons across graphs. More importantly, it does not rely on any distributional assumptions, other than the universally accepted definition of a clustered graph. Empirically, our test is shown to be more responsive to graph structure than other competing tests