2,061 research outputs found
Localization Transition of Biased Random Walks on Random Networks
We study random walks on large random graphs that are biased towards a
randomly chosen but fixed target node. We show that a critical bias strength
b_c exists such that most walks find the target within a finite time when
b>b_c. For b<b_c, a finite fraction of walks drifts off to infinity before
hitting the target. The phase transition at b=b_c is second order, but finite
size behavior is complex and does not obey the usual finite size scaling
ansatz. By extending rigorous results for biased walks on Galton-Watson trees,
we give the exact analytical value for b_c and verify it by large scale
simulations.Comment: 4 pages, includes 4 figure
Random acyclic networks
Directed acyclic graphs are a fundamental class of networks that includes
citation networks, food webs, and family trees, among others. Here we define a
random graph model for directed acyclic graphs and give solutions for a number
of the model's properties, including connection probabilities and component
sizes, as well as a fast algorithm for simulating the model on a computer. We
compare the predictions of the model to a real-world network of citations
between physics papers and find surprisingly good agreement, suggesting that
the structure of the real network may be quite well described by the random
graph.Comment: 4 pages, 2 figure
Interfaces and the edge percolation map of random directed networks
The traditional node percolation map of directed networks is reanalyzed in
terms of edges. In the percolated phase, edges can mainly organize into five
distinct giant connected components, interfaces bridging the communication of
nodes in the strongly connected component and those in the in- and
out-components. Formal equations for the relative sizes in number of edges of
these giant structures are derived for arbitrary joint degree distributions in
the presence of local and two-point correlations. The uncorrelated null model
is fully solved analytically and compared against simulations, finding an
excellent agreement between the theoretical predictions and the edge
percolation map of synthetically generated networks with exponential or
scale-free in-degree distribution and exponential out-degree distribution.
Interfaces, and their internal organization giving place from "hairy ball"
percolation landscapes to bottleneck straits, could bring new light to the
discussion of how structure is interwoven with functionality, in particular in
flow networks.Comment: 20 pages, 4 figure
Properties of Random Graphs with Hidden Color
We investigate in some detail a recently suggested general class of ensembles
of sparse undirected random graphs based on a hidden stub-coloring, with or
without the restriction to nondegenerate graphs. The calculability of local and
global structural properties of graphs from the resulting ensembles is
demonstrated. Cluster size statistics are derived with generating function
techniques, yielding a well-defined percolation threshold. Explicit rules are
derived for the enumeration of small subgraphs. Duality and redundancy is
discussed, and subclasses corresponding to commonly studied models are
identified.Comment: 14 pages, LaTeX, no figure
Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?
We study the Laplacian operator of an uncorrelated random network and, as an
application, consider hopping processes (diffusion, random walks, signal
propagation, etc.) on networks. We develop a strict approach to these problems.
We derive an exact closed set of integral equations, which provide the averages
of the Laplacian operator's resolvent. This enables us to describe the
propagation of a signal and random walks on the network. We show that the
determining parameter in this problem is the minimum degree of vertices
in the network and that the high-degree part of the degree distribution is not
that essential. The position of the lower edge of the Laplacian spectrum
appears to be the same as in the regular Bethe lattice with the
coordination number . Namely, if , and
if . In both these cases the density of eigenvalues
as , but the limiting behaviors near
are very different. In terms of a distance from a starting vertex,
the hopping propagator is a steady moving Gaussian, broadening with time. This
picture qualitatively coincides with that for a regular Bethe lattice. Our
analytical results include the spectral density near
and the long-time asymptotics of the autocorrelator and the
propagator.Comment: 25 pages, 4 figure
Giant strongly connected component of directed networks
We describe how to calculate the sizes of all giant connected components of a
directed graph, including the {\em strongly} connected one. Just to the class
of directed networks, in particular, belongs the World Wide Web. The results
are obtained for graphs with statistically uncorrelated vertices and an
arbitrary joint in,out-degree distribution . We show that if
does not factorize, the relative size of the giant strongly
connected component deviates from the product of the relative sizes of the
giant in- and out-components. The calculations of the relative sizes of all the
giant components are demonstrated using the simplest examples. We explain that
the giant strongly connected component may be less resilient to random damage
than the giant weakly connected one.Comment: 4 pages revtex, 4 figure
Effects of geometry variations on the performance of podded propulsors
This paper presents results and analyses of an experimental study into the effects of geometric parameters on the propulsive characteristics of puller and pusher podded propulsors in straight course open water conditions. Five geometric parameters were chosen for the current study and a design of experiment technique was used to design a series of 16 pods that combined the parameters. Tests on the 16 different pod-strut-propeller combinations in puller and pusher configurations were completed using a custom designed podded propeller test rig. The dynamometry consisted of a six-component global dynamometer and a three-component pod dynamometer. The test rig was used to measure the thrust and torque of the propellers, and forces and moments on the whole unit in the three orthogonal directions. The design of experiment analysis technique was then used to identify the most significant geometric parameters and interaction of parameters that affect propeller thrust, torque and efficiency as well as unit thrust and efficiency in both the puller and pusher configurations. An uncertainty analysis of the measurements is also presented
Generation of uncorrelated random scale-free networks
Uncorrelated random scale-free networks are useful null models to check the
accuracy an the analytical solutions of dynamical processes defined on complex
networks. We propose and analyze a model capable to generate random
uncorrelated scale-free networks with no multiple and self-connections. The
model is based on the classical configuration model, with an additional
restriction on the maximum possible degree of the vertices. We check
numerically that the proposed model indeed generates scale-free networks with
no two and three vertex correlations, as measured by the average degree of the
nearest neighbors and the clustering coefficient of the vertices of degree ,
respectively
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