994 research outputs found
Multistep greedy algorithm identifies community structure in real-world and computer-generated networks
We have recently introduced a multistep extension of the greedy algorithm for
modularity optimization. The extension is based on the idea that merging l
pairs of communities (l>1) at each iteration prevents premature condensation
into few large communities. Here, an empirical formula is presented for the
choice of the step width l that generates partitions with (close to) optimal
modularity for 17 real-world and 1100 computer-generated networks. Furthermore,
an in-depth analysis of the communities of two real-world networks (the
metabolic network of the bacterium E. coli and the graph of coappearing words
in the titles of papers coauthored by Martin Karplus) provides evidence that
the partition obtained by the multistep greedy algorithm is superior to the one
generated by the original greedy algorithm not only with respect to modularity
but also according to objective criteria. In other words, the multistep
extension of the greedy algorithm reduces the danger of getting trapped in
local optima of modularity and generates more reasonable partitions.Comment: 17 pages, 2 figure
Identifying network communities with a high resolution
Community structure is an important property of complex networks. An
automatic discovery of such structure is a fundamental task in many
disciplines, including sociology, biology, engineering, and computer science.
Recently, several community discovery algorithms have been proposed based on
the optimization of a quantity called modularity (Q). However, the problem of
modularity optimization is NP-hard, and the existing approaches often suffer
from prohibitively long running time or poor quality. Furthermore, it has been
recently pointed out that algorithms based on optimizing Q will have a
resolution limit, i.e., communities below a certain scale may not be detected.
In this research, we first propose an efficient heuristic algorithm, Qcut,
which combines spectral graph partitioning and local search to optimize Q.
Using both synthetic and real networks, we show that Qcut can find higher
modularities and is more scalable than the existing algorithms. Furthermore,
using Qcut as an essential component, we propose a recursive algorithm, HQcut,
to solve the resolution limit problem. We show that HQcut can successfully
detect communities at a much finer scale and with a higher accuracy than the
existing algorithms. Finally, we apply Qcut and HQcut to study a
protein-protein interaction network, and show that the combination of the two
algorithms can reveal interesting biological results that may be otherwise
undetectable.Comment: 14 pages, 5 figures. 1 supplemental file at
http://cic.cs.wustl.edu/qcut/supplemental.pd
Community Detection as an Inference Problem
We express community detection as an inference problem of determining the
most likely arrangement of communities. We then apply belief propagation and
mean-field theory to this problem, and show that this leads to fast, accurate
algorithms for community detection.Comment: 4 pages, 2 figure
Evaluating Local Community Methods in Networks
We present a new benchmarking procedure that is unambiguous and specific to
local community-finding methods, allowing one to compare the accuracy of
various methods. We apply this to new and existing algorithms. A simple class
of synthetic benchmark networks is also developed, capable of testing
properties specific to these local methods.Comment: 8 pages, 9 figures, code included with sourc
The Implementation of the Global Minimum Tax (GloBE): The Need for an Effective Dispute Prevention and Resolution Mechanism
The successful implementation of the Global Anti-Base Erosion (GloBE) rules on aglobal scale cannot be achieved without an international effective dispute prevention and reso-lution mechanism. However, the development of a dispute prevention and resolution frameworkfor the GloBE rules faces significant challenges. This article offers two possible options for aneffective dispute prevention and resolution mechanism: a model based on reciprocal domesticlegislations and the multilateral convention model
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