48 research outputs found
Scaling of internode distances in weighted complex networks
We extend the previously observed scaling equation connecting the internode
distances and nodes' degrees onto the case of weighted networks. We show that
the scaling takes a similar form in the empirical data obtained from networks
characterized by different relations between node's strength and its degree. In
the case of explicit equation for s(k) (e.g. linear or scale-free), the new
coefficients of scaling equation can be easily obtained. We support our
analysis with numerical simulations for Erdos-Renyi random graphs with
different weight distributions.Comment: 9 pages, 4 figures, submitted to International Journal of Modern
Physics
Anomalous oscillations of average transient lifetimes near crises
It is common that the average length of chaotic transients appearing as a
consequence of crises in dynamical systems obeys a power low of scaling with
the distance from the crisis point. It is, however, only a rough trend; in some
cases considerable oscillations can be superimposed on it. In this letter we
report anomalous oscillations due to the intertwined structure of basins of
attraction. We also present a simple geometrical model that gives an estimate
of the period and amplitude of these oscillations. The results obtained within
the model coincide with those yielded by computer simulations of a kicked spin
model and the Henon map.Comment: 5 pages, 4 figure
How to calculate the main characteristics of random uncorrelated networks
We present an analytic formalism describing structural properties of random
uncorrelated networks with arbitrary degree distributions. The formalism allows
to calculate the main network characteristics like: the position of the phase
transition at which a giant component first forms, the mean component size
below the phase transition, the size of the giant component and the average
path length above the phase transition. We apply the approach to classical
random graphs of Erdos and Renyi, single-scale networks with exponential degree
distributions and scale-free networks with arbitrary scaling exponents and
structural cut-offs. In all the cases we obtain a very good agreement between
results of numerical simulations and our analytical predictions.Comment: AIP conference proceedings format, 17 pages, 6 figure
Hierarchical Cont-Bouchaud model
We extend the well-known Cont-Bouchaud model to include a hierarchical
topology of agent's interactions. The influence of hierarchy on system dynamics
is investigated by two models. The first one is based on a multi-level, nested
Erdos-Renyi random graph and individual decisions by agents according to Potts
dynamics. This approach does not lead to a broad return distribution outside a
parameter regime close to the original Cont-Bouchaud model. In the second model
we introduce a limited hierarchical Erdos-Renyi graph, where merging of
clusters at a level h+1 involves only clusters that have merged at the previous
level h and we use the original Cont-Bouchaud agent dynamics on resulting
clusters. The second model leads to a heavy-tail distribution of cluster sizes
and relative price changes in a wide range of connection densities, not only
close to the percolation threshold.Comment: 10 pages, 6 figure