Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular synchronization in complex networks with a gauge Kuramoto model   We modify the Kuramoto model for synchronization on complex networks by
introducing a gauge term that depends on the edge betweenness centrality (BC).
The gauge term introduces additional phase difference between two vertices from
0 to $\pi$ as the BC on the edge between them increases from the minimum to the
maximum in the network. When the network has a modular structure, the model
generates the phase synchronization within each module, however, not over the
entire system. Based on this feature, we can distinguish modules in complex
networks, with relatively little computational time of $\mathcal{O}(NL)$, where
$N$ and $L$ are the number of vertices and edges in the system, respectively.
We also examine the synchronization of the modified Kuramoto model and compare
it with that of the original Kuramoto model in several complex networks.

24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas