10,269 research outputs found
Portraits of Complex Networks
We propose a method for characterizing large complex networks by introducing
a new matrix structure, unique for a given network, which encodes structural
information; provides useful visualization, even for very large networks; and
allows for rigorous statistical comparison between networks. Dynamic processes
such as percolation can be visualized using animations. Applications to graph
theory are discussed, as are generalizations to weighted networks, real-world
network similarity testing, and applicability to the graph isomorphism problem.Comment: 6 pages, 9 figure
Asymmetries arising from the space-filling nature of vascular networks
Cardiovascular networks span the body by branching across many generations of
vessels. The resulting structure delivers blood over long distances to supply
all cells with oxygen via the relatively short-range process of diffusion at
the capillary level. The structural features of the network that accomplish
this density and ubiquity of capillaries are often called space-filling. There
are multiple strategies to fill a space, but some strategies do not lead to
biologically adaptive structures by requiring too much construction material or
space, delivering resources too slowly, or using too much power to move blood
through the system. We empirically measure the structure of real networks (18
humans and 1 mouse) and compare these observations with predictions of model
networks that are space-filling and constrained by a few guiding biological
principles. We devise a numerical method that enables the investigation of
space-filling strategies and determination of which biological principles
influence network structure. Optimization for only a single principle creates
unrealistic networks that represent an extreme limit of the possible structures
that could be observed in nature. We first study these extreme limits for two
competing principles, minimal total material and minimal path lengths. We
combine these two principles and enforce various thresholds for balance in the
network hierarchy, which provides a novel approach that highlights the
trade-offs faced by biological networks and yields predictions that better
match our empirical data.Comment: 17 pages, 15 figure
Subgraph covers -- An information theoretic approach to motif analysis in networks
Many real world networks contain a statistically surprising number of certain
subgraphs, called network motifs. In the prevalent approach to motif analysis,
network motifs are detected by comparing subgraph frequencies in the original
network with a statistical null model. In this paper we propose an alternative
approach to motif analysis where network motifs are defined to be connectivity
patterns that occur in a subgraph cover that represents the network using
minimal total information. A subgraph cover is defined to be a set of subgraphs
such that every edge of the graph is contained in at least one of the subgraphs
in the cover. Some recently introduced random graph models that can incorporate
significant densities of motifs have natural formulations in terms of subgraph
covers and the presented approach can be used to match networks with such
models. To prove the practical value of our approach we also present a
heuristic for the resulting NP-hard optimization problem and give results for
several real world networks.Comment: 10 pages, 7 tables, 1 Figur
Classifying pairs with trees for supervised biological network inference
Networks are ubiquitous in biology and computational approaches have been
largely investigated for their inference. In particular, supervised machine
learning methods can be used to complete a partially known network by
integrating various measurements. Two main supervised frameworks have been
proposed: the local approach, which trains a separate model for each network
node, and the global approach, which trains a single model over pairs of nodes.
Here, we systematically investigate, theoretically and empirically, the
exploitation of tree-based ensemble methods in the context of these two
approaches for biological network inference. We first formalize the problem of
network inference as classification of pairs, unifying in the process
homogeneous and bipartite graphs and discussing two main sampling schemes. We
then present the global and the local approaches, extending the later for the
prediction of interactions between two unseen network nodes, and discuss their
specializations to tree-based ensemble methods, highlighting their
interpretability and drawing links with clustering techniques. Extensive
computational experiments are carried out with these methods on various
biological networks that clearly highlight that these methods are competitive
with existing methods.Comment: 22 page
Recovering complete and draft population genomes from metagenome datasets.
Assembly of metagenomic sequence data into microbial genomes is of fundamental value to improving our understanding of microbial ecology and metabolism by elucidating the functional potential of hard-to-culture microorganisms. Here, we provide a synthesis of available methods to bin metagenomic contigs into species-level groups and highlight how genetic diversity, sequencing depth, and coverage influence binning success. Despite the computational cost on application to deeply sequenced complex metagenomes (e.g., soil), covarying patterns of contig coverage across multiple datasets significantly improves the binning process. We also discuss and compare current genome validation methods and reveal how these methods tackle the problem of chimeric genome bins i.e., sequences from multiple species. Finally, we explore how population genome assembly can be used to uncover biogeographic trends and to characterize the effect of in situ functional constraints on the genome-wide evolution
Non-parametric resampling of random walks for spectral network clustering
Parametric resampling schemes have been recently introduced in complex
network analysis with the aim of assessing the statistical significance of
graph clustering and the robustness of community partitions. We propose here a
method to replicate structural features of complex networks based on the
non-parametric resampling of the transition matrix associated with an unbiased
random walk on the graph. We test this bootstrapping technique on synthetic and
real-world modular networks and we show that the ensemble of replicates
obtained through resampling can be used to improve the performance of standard
spectral algorithms for community detection.Comment: 5 pages, 2 figure
Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)
Although the ``scale-free'' literature is large and growing, it gives neither
a precise definition of scale-free graphs nor rigorous proofs of many of their
claimed properties. In fact, it is easily shown that the existing theory has
many inherent contradictions and verifiably false claims. In this paper, we
propose a new, mathematically precise, and structural definition of the extent
to which a graph is scale-free, and prove a series of results that recover many
of the claimed properties while suggesting the potential for a rich and
interesting theory. With this definition, scale-free (or its opposite,
scale-rich) is closely related to other structural graph properties such as
various notions of self-similarity (or respectively, self-dissimilarity).
Scale-free graphs are also shown to be the likely outcome of random
construction processes, consistent with the heuristic definitions implicit in
existing random graph approaches. Our approach clarifies much of the confusion
surrounding the sensational qualitative claims in the scale-free literature,
and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet
Mathematics (2005
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