Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization and centrality in networks   Eigenvector centrality is a common measure of the importance of nodes in a
network. Here we show that under common conditions the eigenvector centrality
displays a localization transition that causes most of the weight of the
centrality to concentrate on a small number of nodes in the network. In this
regime the measure is no longer useful for distinguishing among the remaining
nodes and its efficacy as a network metric is impaired. As a remedy, we propose
an alternative centrality measure based on the nonbacktracking matrix, which
gives results closely similar to the standard eigenvector centrality in dense
networks where the latter is well behaved, but avoids localization and gives
useful results in regimes where the standard centrality fails.

11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph