Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On irreversible spread of influence in edge-weighted graphs   Various kinds of spread of influence occur in real world social and virtual
networks. These phenomena are formulated by activation processes and
irreversible dynamic monopolies in combinatorial graphs representing the
topology of the networks. In most cases the nature of influence is weighted and
the spread of influence depends on the weight of edges. The ordinary
formulation and results for dynamic monopolies do not work for such models. In
this paper we present a graph theoretical analysis for spread of weighted
influence and mention a real world example realizing the activation model with
weighted influence. Then we obtain some extremal bounds and algorithmic results
for activation process and dynamic monopolies in directed and undirected graphs
with weighted edges.

30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph