Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Definiteness of the Weighted Laplacian and its Connection to
  Effective Resistance   This work explores the definiteness of the weighted graph Laplacian matrix
with negative edge weights. The definiteness of the weighted Laplacian is
studied in terms of certain matrices that are related via congruent and
similarity transformations. For a graph with a single negative weight edge, we
show that the weighted Laplacian becomes indefinite if the magnitude of the
negative weight is less than the inverse of the effective resistance between
the two incident nodes. This result is extended to multiple negative weight
edges. The utility of these results are demonstrated in a weighted consensus
network where appropriately placed negative weight edges can induce a
clustering behavior for the protocol.

9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat