91,774 research outputs found
A General Framework for Complex Network Applications
Complex network theory has been applied to solving practical problems from
different domains. In this paper, we present a general framework for complex
network applications. The keys of a successful application are a thorough
understanding of the real system and a correct mapping of complex network
theory to practical problems in the system. Despite of certain limitations
discussed in this paper, complex network theory provides a foundation on which
to develop powerful tools in analyzing and optimizing large interconnected
systems.Comment: 8 page
Communities in Networks
We survey some of the concepts, methods, and applications of community
detection, which has become an increasingly important area of network science.
To help ease newcomers into the field, we provide a guide to available
methodology and open problems, and discuss why scientists from diverse
backgrounds are interested in these problems. As a running theme, we emphasize
the connections of community detection to problems in statistical physics and
computational optimization.Comment: survey/review article on community structure in networks; published
version is available at
http://people.maths.ox.ac.uk/~porterm/papers/comnotices.pd
Tensor Spectral Clustering for Partitioning Higher-order Network Structures
Spectral graph theory-based methods represent an important class of tools for
studying the structure of networks. Spectral methods are based on a first-order
Markov chain derived from a random walk on the graph and thus they cannot take
advantage of important higher-order network substructures such as triangles,
cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering
(TSC) algorithm that allows for modeling higher-order network structures in a
graph partitioning framework. Our TSC algorithm allows the user to specify
which higher-order network structures (cycles, feed-forward loops, etc.) should
be preserved by the network clustering. Higher-order network structures of
interest are represented using a tensor, which we then partition by developing
a multilinear spectral method. Our framework can be applied to discovering
layered flows in networks as well as graph anomaly detection, which we
illustrate on synthetic networks. In directed networks, a higher-order
structure of particular interest is the directed 3-cycle, which captures
feedback loops in networks. We demonstrate that our TSC algorithm produces
large partitions that cut fewer directed 3-cycles than standard spectral
clustering algorithms.Comment: SDM 201
Ubiquitousness of link-density and link-pattern communities in real-world networks
Community structure appears to be an intrinsic property of many complex
real-world networks. However, recent work shows that real-world networks reveal
even more sophisticated modules than classical cohesive (link-density)
communities. In particular, networks can also be naturally partitioned
according to similar patterns of connectedness among the nodes, revealing
link-pattern communities. We here propose a propagation based algorithm that
can extract both link-density and link-pattern communities, without any prior
knowledge of the true structure. The algorithm was first validated on different
classes of synthetic benchmark networks with community structure, and also on
random networks. We have further applied the algorithm to different social,
information, technological and biological networks, where it indeed reveals
meaningful (composites of) link-density and link-pattern communities. The
results thus seem to imply that, similarly as link-density counterparts,
link-pattern communities appear ubiquitous in nature and design
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