14,118 research outputs found
Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems
To comprehend the hierarchical organization of large integrated systems, we
introduce the hierarchical map equation, which reveals multilevel structures in
networks. In this information-theoretic approach, we exploit the duality
between compression and pattern detection; by compressing a description of a
random walker as a proxy for real flow on a network, we find regularities in
the network that induce this system-wide flow. Finding the shortest multilevel
description of the random walker therefore gives us the best hierarchical
clustering of the network, the optimal number of levels and modular partition
at each level, with respect to the dynamics on the network. With a novel search
algorithm, we extract and illustrate the rich multilevel organization of
several large social and biological networks. For example, from the global air
traffic network we uncover countries and continents, and from the pattern of
scientific communication we reveal more than 100 scientific fields organized in
four major disciplines: life sciences, physical sciences, ecology and earth
sciences, and social sciences. In general, we find shallow hierarchical
structures in globally interconnected systems, such as neural networks, and
rich multilevel organizations in systems with highly separated regions, such as
road networks.Comment: 11 pages, 5 figures. For associated code, see
http://www.tp.umu.se/~rosvall/code.htm
Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems
Unveiling the community structure of networks is a powerful methodology to
comprehend interconnected systems across the social and natural sciences. To
identify different types of functional modules in interaction data aggregated
in a single network layer, researchers have developed many powerful methods.
For example, flow-based methods have proven useful for identifying modular
dynamics in weighted and directed networks that capture constraints on flow in
the systems they represent. However, many networked systems consist of agents
or components that exhibit multiple layers of interactions. Inevitably,
representing this intricate network of networks as a single aggregated network
leads to information loss and may obscure the actual organization. Here we
propose a method based on compression of network flows that can identify
modular flows in non-aggregated multilayer networks. Our numerical experiments
on synthetic networks show that the method can accurately identify modules that
cannot be identified in aggregated networks or by analyzing the layers
separately. We capitalize on our findings and reveal the community structure of
two multilayer collaboration networks: scientists affiliated to the Pierre
Auger Observatory and scientists publishing works on networks on the arXiv.
Compared to conventional aggregated methods, the multilayer method reveals
smaller modules with more overlap that better capture the actual organization
Model selection and hypothesis testing for large-scale network models with overlapping groups
The effort to understand network systems in increasing detail has resulted in
a diversity of methods designed to extract their large-scale structure from
data. Unfortunately, many of these methods yield diverging descriptions of the
same network, making both the comparison and understanding of their results a
difficult challenge. A possible solution to this outstanding issue is to shift
the focus away from ad hoc methods and move towards more principled approaches
based on statistical inference of generative models. As a result, we face
instead the more well-defined task of selecting between competing generative
processes, which can be done under a unified probabilistic framework. Here, we
consider the comparison between a variety of generative models including
features such as degree correction, where nodes with arbitrary degrees can
belong to the same group, and community overlap, where nodes are allowed to
belong to more than one group. Because such model variants possess an
increasing number of parameters, they become prone to overfitting. In this
work, we present a method of model selection based on the minimum description
length criterion and posterior odds ratios that is capable of fully accounting
for the increased degrees of freedom of the larger models, and selects the best
one according to the statistical evidence available in the data. In applying
this method to many empirical unweighted networks from different fields, we
observe that community overlap is very often not supported by statistical
evidence and is selected as a better model only for a minority of them. On the
other hand, we find that degree correction tends to be almost universally
favored by the available data, implying that intrinsic node proprieties (as
opposed to group properties) are often an essential ingredient of network
formation.Comment: 20 pages,7 figures, 1 tabl
Detecting Cohesive and 2-mode Communities in Directed and Undirected Networks
Networks are a general language for representing relational information among
objects. An effective way to model, reason about, and summarize networks, is to
discover sets of nodes with common connectivity patterns. Such sets are
commonly referred to as network communities. Research on network community
detection has predominantly focused on identifying communities of densely
connected nodes in undirected networks.
In this paper we develop a novel overlapping community detection method that
scales to networks of millions of nodes and edges and advances research along
two dimensions: the connectivity structure of communities, and the use of edge
directedness for community detection. First, we extend traditional definitions
of network communities by building on the observation that nodes can be densely
interlinked in two different ways: In cohesive communities nodes link to each
other, while in 2-mode communities nodes link in a bipartite fashion, where
links predominate between the two partitions rather than inside them. Our
method successfully detects both 2-mode as well as cohesive communities, that
may also overlap or be hierarchically nested. Second, while most existing
community detection methods treat directed edges as though they were
undirected, our method accounts for edge directions and is able to identify
novel and meaningful community structures in both directed and undirected
networks, using data from social, biological, and ecological domains.Comment: Published in the proceedings of WSDM '1
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