224 research outputs found
Finding community structure in networks using the eigenvectors of matrices
We consider the problem of detecting communities or modules in networks,
groups of vertices with a higher-than-average density of edges connecting them.
Previous work indicates that a robust approach to this problem is the
maximization of the benefit function known as "modularity" over possible
divisions of a network. Here we show that this maximization process can be
written in terms of the eigenspectrum of a matrix we call the modularity
matrix, which plays a role in community detection similar to that played by the
graph Laplacian in graph partitioning calculations. This result leads us to a
number of possible algorithms for detecting community structure, as well as
several other results, including a spectral measure of bipartite structure in
networks and a new centrality measure that identifies those vertices that
occupy central positions within the communities to which they belong. The
algorithms and measures proposed are illustrated with applications to a variety
of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio
Experimental evidence for the sensitivity of the air-shower radio signal to the longitudinal shower development
We observe a correlation between the slope of radio lateral distributions,
and the mean muon pseudorapidity of 59 individual cosmic-ray-air-shower events.
The radio lateral distributions are measured with LOPES, a digital radio
interferometer co-located with the multi-detector-air-shower array
KASCADE-Grande, which includes a muon-tracking detector. The result proves
experimentally that radio measurements are sensitive to the longitudinal
development of cosmic-ray air-showers. This is one of the main prerequisites
for using radio arrays for ultra-high-energy particle physics and astrophysics.Comment: 6 pages, 5 figures, accepted for publication by Physical Review
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