64,990 research outputs found
Hierarchy measure for complex networks
Nature, technology and society are full of complexity arising from the
intricate web of the interactions among the units of the related systems (e.g.,
proteins, computers, people). Consequently, one of the most successful recent
approaches to capturing the fundamental features of the structure and dynamics
of complex systems has been the investigation of the networks associated with
the above units (nodes) together with their relations (edges). Most complex
systems have an inherently hierarchical organization and, correspondingly, the
networks behind them also exhibit hierarchical features. Indeed, several papers
have been devoted to describing this essential aspect of networks, however,
without resulting in a widely accepted, converging concept concerning the
quantitative characterization of the level of their hierarchy. Here we develop
an approach and propose a quantity (measure) which is simple enough to be
widely applicable, reveals a number of universal features of the organization
of real-world networks and, as we demonstrate, is capable of capturing the
essential features of the structure and the degree of hierarchy in a complex
network. The measure we introduce is based on a generalization of the m-reach
centrality, which we first extend to directed/partially directed graphs. Then,
we define the global reaching centrality (GRC), which is the difference between
the maximum and the average value of the generalized reach centralities over
the network. We investigate the behavior of the GRC considering both a
synthetic model with an adjustable level of hierarchy and real networks.
Results for real networks show that our hierarchy measure is related to the
controllability of the given system. We also propose a visualization procedure
for large complex networks that can be used to obtain an overall qualitative
picture about the nature of their hierarchical structure.Comment: 29 pages, 9 figures, 4 table
ModuLand plug-in for Cytoscape: determination of hierarchical layers of overlapping network modules and community centrality
Summary: The ModuLand plug-in provides Cytoscape users an algorithm for
determining extensively overlapping network modules. Moreover, it identifies
several hierarchical layers of modules, where meta-nodes of the higher
hierarchical layer represent modules of the lower layer. The tool assigns
module cores, which predict the function of the whole module, and determines
key nodes bridging two or multiple modules. The plug-in has a detailed
JAVA-based graphical interface with various colouring options. The ModuLand
tool can run on Windows, Linux, or Mac OS. We demonstrate its use on protein
structure and metabolic networks. Availability: The plug-in and its user guide
can be downloaded freely from: http://www.linkgroup.hu/modules.php. Contact:
[email protected] Supplementary information: Supplementary
information is available at Bioinformatics online.Comment: 39 pages, 1 figure and a Supplement with 9 figures and 10 table
A model for dynamic communicators
We develop and test an intuitively simple dynamic network model to describe the type of time-varying connectivity structure present in many technological settings. The model assumes that nodes have an inherent hierarchy governing the emergence of new connections. This idea draws on newly established concepts in online human behaviour concerning the existence of discussion catalysts, who initiate long threads, and online leaders, who trigger feedback. We show that the model captures an important property found in e-mail and voice call data â âdynamic communicatorsâ with sufficient foresight or impact to generate effective links and having an influence that is grossly underestimated by static measures based on snaphots or aggregated data
Modeling the emergence of modular leadership hierarchy during the collective motion of herds made of harems
Gregarious animals need to make collective decisions in order to keep their
cohesiveness. Several species of them live in multilevel societies, and form
herds composed of smaller communities. We present a model for the development
of a leadership hierarchy in a herd consisting of loosely connected sub-groups
(e.g. harems) by combining self organization and social dynamics. It starts
from unfamiliar individuals without relationships and reproduces the emergence
of a hierarchical and modular leadership network that promotes an effective
spreading of the decisions from more capable individuals to the others, and
thus gives rise to a beneficial collective decision. Our results stemming from
the model are in a good agreement with our observations of a Przewalski horse
herd (Hortob\'agy, Hungary). We find that the harem-leader to harem-member
ratio observed in Przewalski horses corresponds to an optimal network in this
approach regarding common success, and that the observed and modeled harem size
distributions are close to a lognormal.Comment: 18 pages, 7 figures, J. Stat. Phys. (2014
Embedding Graphs under Centrality Constraints for Network Visualization
Visual rendering of graphs is a key task in the mapping of complex network
data. Although most graph drawing algorithms emphasize aesthetic appeal,
certain applications such as travel-time maps place more importance on
visualization of structural network properties. The present paper advocates two
graph embedding approaches with centrality considerations to comply with node
hierarchy. The problem is formulated first as one of constrained
multi-dimensional scaling (MDS), and it is solved via block coordinate descent
iterations with successive approximations and guaranteed convergence to a KKT
point. In addition, a regularization term enforcing graph smoothness is
incorporated with the goal of reducing edge crossings. A second approach
leverages the locally-linear embedding (LLE) algorithm which assumes that the
graph encodes data sampled from a low-dimensional manifold. Closed-form
solutions to the resulting centrality-constrained optimization problems are
determined yielding meaningful embeddings. Experimental results demonstrate the
efficacy of both approaches, especially for visualizing large networks on the
order of thousands of nodes.Comment: Submitted to IEEE Transactions on Visualization and Computer Graphic
Extracting tag hierarchies
Tagging items with descriptive annotations or keywords is a very natural way
to compress and highlight information about the properties of the given entity.
Over the years several methods have been proposed for extracting a hierarchy
between the tags for systems with a "flat", egalitarian organization of the
tags, which is very common when the tags correspond to free words given by
numerous independent people. Here we present a complete framework for automated
tag hierarchy extraction based on tag occurrence statistics. Along with
proposing new algorithms, we are also introducing different quality measures
enabling the detailed comparison of competing approaches from different
aspects. Furthermore, we set up a synthetic, computer generated benchmark
providing a versatile tool for testing, with a couple of tunable parameters
capable of generating a wide range of test beds. Beside the computer generated
input we also use real data in our studies, including a biological example with
a pre-defined hierarchy between the tags. The encouraging similarity between
the pre-defined and reconstructed hierarchy, as well as the seemingly
meaningful hierarchies obtained for other real systems indicate that tag
hierarchy extraction is a very promising direction for further research with a
great potential for practical applications.Comment: 25 pages with 21 pages of supporting information, 25 figure
Comparing the hierarchy of keywords in on-line news portals
The tagging of on-line content with informative keywords is a widespread
phenomenon from scientific article repositories through blogs to on-line news
portals. In most of the cases, the tags on a given item are free words chosen
by the authors independently. Therefore, relations among keywords in a
collection of news items is unknown. However, in most cases the topics and
concepts described by these keywords are forming a latent hierarchy, with the
more general topics and categories at the top, and more specialised ones at the
bottom. Here we apply a recent, cooccurrence-based tag hierarchy extraction
method to sets of keywords obtained from four different on-line news portals.
The resulting hierarchies show substantial differences not just in the topics
rendered as important (being at the top of the hierarchy) or of less interest
(categorised low in the hierarchy), but also in the underlying network
structure. This reveals discrepancies between the plausible keyword association
frameworks in the studied news portals
- âŠ