975 research outputs found
Module identification in bipartite and directed networks
Modularity is one of the most prominent properties of real-world complex
networks. Here, we address the issue of module identification in two important
classes of networks: bipartite networks and directed unipartite networks. Nodes
in bipartite networks are divided into two non-overlapping sets, and the links
must have one end node from each set. Directed unipartite networks only have
one type of nodes, but links have an origin and an end. We show that directed
unipartite networks can be conviniently represented as bipartite networks for
module identification purposes. We report a novel approach especially suited
for module detection in bipartite networks, and define a set of random networks
that enable us to validate the new approach
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
A paradox in community detection
Recent research has shown that virtually all algorithms aimed at the
identification of communities in networks are affected by the same main
limitation: the impossibility to detect communities, even when these are
well-defined, if the average value of the difference between internal and
external node degrees does not exceed a strictly positive value, in literature
known as detectability threshold. Here, we counterintuitively show that the
value of this threshold is inversely proportional to the intrinsic quality of
communities: the detection of well-defined modules is thus more difficult than
the identification of ill-defined communities.Comment: 5 pages, 3 figure
Benchmark graphs for testing community detection algorithms
Community structure is one of the most important features of real networks
and reveals the internal organization of the nodes. Many algorithms have been
proposed but the crucial issue of testing, i.e. the question of how good an
algorithm is, with respect to others, is still open. Standard tests include the
analysis of simple artificial graphs with a built-in community structure, that
the algorithm has to recover. However, the special graphs adopted in actual
tests have a structure that does not reflect the real properties of nodes and
communities found in real networks. Here we introduce a new class of benchmark
graphs, that account for the heterogeneity in the distributions of node degrees
and of community sizes. We use this new benchmark to test two popular methods
of community detection, modularity optimization and Potts model clustering. The
results show that the new benchmark poses a much more severe test to algorithms
than standard benchmarks, revealing limits that may not be apparent at a first
analysis.Comment: 6 pages, 8 figures. Extended version published on Physical Review E.
The code to build the new benchmark graphs can be downloaded from
http://santo.fortunato.googlepages.com/inthepress
Impact of constrained rewiring on network structure and node dynamics
In this paper, we study an adaptive spatial network. We consider a susceptible-infected-susceptible (SIS) epidemic on the network, with a link or contact rewiring process constrained by spatial proximity. In particular, we assume that susceptible nodes break links with infected nodes independently of distance and reconnect at random to susceptible nodes available within a given radius. By systematically manipulating this radius we investigate the impact of rewiring on the structure of the network and characteristics of the epidemic.We adopt a step-by-step approach whereby we first study the impact of rewiring on the network structure in the absence of an epidemic, then with nodes assigned a disease status but without disease dynamics, and finally running network and epidemic dynamics simultaneously. In the case of no labeling and no epidemic dynamics, we provide both analytic and semianalytic formulas for the value of clustering achieved in the network. Our results also show that the rewiring radius and the network’s initial structure have a pronounced effect on the endemic equilibrium, with increasingly large rewiring radiuses yielding smaller disease prevalence
Quantum Tunneling Detection of Two-photon and Two-electron Processes
We analyze the operation of a quantum tunneling detector coupled to a
coherent conductor. We demonstrate that in a certain energy range the output of
the detector is determined by two-photon processes, two-electron processes and
the interference of the two. We show how the individual contributions of these
processes can be resolved in experiments.Comment: 4 pages, 4 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
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
Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities
Many complex networks display a mesoscopic structure with groups of nodes
sharing many links with the other nodes in their group and comparatively few
with nodes of different groups. This feature is known as community structure
and encodes precious information about the organization and the function of the
nodes. Many algorithms have been proposed but it is not yet clear how they
should be tested. Recently we have proposed a general class of undirected and
unweighted benchmark graphs, with heterogenous distributions of node degree and
community size. An increasing attention has been recently devoted to develop
algorithms able to consider the direction and the weight of the links, which
require suitable benchmark graphs for testing. In this paper we extend the
basic ideas behind our previous benchmark to generate directed and weighted
networks with built-in community structure. We also consider the possibility
that nodes belong to more communities, a feature occurring in real systems,
like, e. g., social networks. As a practical application, we show how
modularity optimization performs on our new benchmark.Comment: 9 pages, 13 figures. Final version published in Physical Review E.
The code to create the benchmark graphs can be freely downloaded from
http://santo.fortunato.googlepages.com/inthepress
Comments to Public Consultation Document: Global Anti-Base Erosion Proposal (“GloBE”) - Pillar Two
- …