22,369 research outputs found
The structure and function of complex networks
Inspired by empirical studies of networked systems such as the Internet,
social networks, and biological networks, researchers have in recent years
developed a variety of techniques and models to help us understand or predict
the behavior of these systems. Here we review developments in this field,
including such concepts as the small-world effect, degree distributions,
clustering, network correlations, random graph models, models of network growth
and preferential attachment, and dynamical processes taking place on networks.Comment: Review article, 58 pages, 16 figures, 3 tables, 429 references,
published in SIAM Review (2003
Finding community structure in very large networks
The discovery and analysis of community structure in networks is a topic of
considerable recent interest within the physics community, but most methods
proposed so far are unsuitable for very large networks because of their
computational cost. Here we present a hierarchical agglomeration algorithm for
detecting community structure which is faster than many competing algorithms:
its running time on a network with n vertices and m edges is O(m d log n) where
d is the depth of the dendrogram describing the community structure. Many
real-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in
which case our algorithm runs in essentially linear time, O(n log^2 n). As an
example of the application of this algorithm we use it to analyze a network of
items for sale on the web-site of a large online retailer, items in the network
being linked if they are frequently purchased by the same buyer. The network
has more than 400,000 vertices and 2 million edges. We show that our algorithm
can extract meaningful communities from this network, revealing large-scale
patterns present in the purchasing habits of customers
Bi-Objective Community Detection (BOCD) in Networks using Genetic Algorithm
A lot of research effort has been put into community detection from all
corners of academic interest such as physics, mathematics and computer science.
In this paper I have proposed a Bi-Objective Genetic Algorithm for community
detection which maximizes modularity and community score. Then the results
obtained for both benchmark and real life data sets are compared with other
algorithms using the modularity and MNI performance metrics. The results show
that the BOCD algorithm is capable of successfully detecting community
structure in both real life and synthetic datasets, as well as improving upon
the performance of previous techniques.Comment: 11 pages, 3 Figures, 3 Tables. arXiv admin note: substantial text
overlap with arXiv:0906.061
Algorithmic and Statistical Perspectives on Large-Scale Data Analysis
In recent years, ideas from statistics and scientific computing have begun to
interact in increasingly sophisticated and fruitful ways with ideas from
computer science and the theory of algorithms to aid in the development of
improved worst-case algorithms that are useful for large-scale scientific and
Internet data analysis problems. In this chapter, I will describe two recent
examples---one having to do with selecting good columns or features from a (DNA
Single Nucleotide Polymorphism) data matrix, and the other having to do with
selecting good clusters or communities from a data graph (representing a social
or information network)---that drew on ideas from both areas and that may serve
as a model for exploiting complementary algorithmic and statistical
perspectives in order to solve applied large-scale data analysis problems.Comment: 33 pages. To appear in Uwe Naumann and Olaf Schenk, editors,
"Combinatorial Scientific Computing," Chapman and Hall/CRC Press, 201
Structure of Heterogeneous Networks
Heterogeneous networks play a key role in the evolution of communities and
the decisions individuals make. These networks link different types of
entities, for example, people and the events they attend. Network analysis
algorithms usually project such networks unto simple graphs composed of
entities of a single type. In the process, they conflate relations between
entities of different types and loose important structural information. We
develop a mathematical framework that can be used to compactly represent and
analyze heterogeneous networks that combine multiple entity and link types. We
generalize Bonacich centrality, which measures connectivity between nodes by
the number of paths between them, to heterogeneous networks and use this
measure to study network structure. Specifically, we extend the popular
modularity-maximization method for community detection to use this centrality
metric. We also rank nodes based on their connectivity to other nodes. One
advantage of this centrality metric is that it has a tunable parameter we can
use to set the length scale of interactions. By studying how rankings change
with this parameter allows us to identify important nodes in the network. We
apply the proposed method to analyze the structure of several heterogeneous
networks. We show that exploiting additional sources of evidence corresponding
to links between, as well as among, different entity types yields new insights
into network structure
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