2,628 research outputs found
Graph Annotations in Modeling Complex Network Topologies
The coarsest approximation of the structure of a complex network, such as the
Internet, is a simple undirected unweighted graph. This approximation, however,
loses too much detail. In reality, objects represented by vertices and edges in
such a graph possess some non-trivial internal structure that varies across and
differentiates among distinct types of links or nodes. In this work, we
abstract such additional information as network annotations. We introduce a
network topology modeling framework that treats annotations as an extended
correlation profile of a network. Assuming we have this profile measured for a
given network, we present an algorithm to rescale it in order to construct
networks of varying size that still reproduce the original measured annotation
profile.
Using this methodology, we accurately capture the network properties
essential for realistic simulations of network applications and protocols, or
any other simulations involving complex network topologies, including modeling
and simulation of network evolution. We apply our approach to the Autonomous
System (AS) topology of the Internet annotated with business relationships
between ASs. This topology captures the large-scale structure of the Internet.
In depth understanding of this structure and tools to model it are cornerstones
of research on future Internet architectures and designs. We find that our
techniques are able to accurately capture the structure of annotation
correlations within this topology, thus reproducing a number of its important
properties in synthetically-generated random graphs
Understanding Internet topology: principles, models, and validation
Building on a recent effort that combines a first-principles approach to modeling router-level connectivity with a more pragmatic use of statistics and graph theory, we show in this paper that for the Internet, an improved understanding of its physical infrastructure is possible by viewing the physical connectivity as an annotated graph that delivers raw connectivity and bandwidth to the upper layers in the TCP/IP protocol stack, subject to practical constraints (e.g., router technology) and economic considerations (e.g., link costs). More importantly, by relying on data from Abilene, a Tier-1 ISP, and the Rocketfuel project, we provide empirical evidence in support of the proposed approach and its consistency with networking reality. To illustrate its utility, we: 1) show that our approach provides insight into the origin of high variability in measured or inferred router-level maps; 2) demonstrate that it easily accommodates the incorporation of additional objectives of network design (e.g., robustness to router failure); and 3) discuss how it complements ongoing community efforts to reverse-engineer the Internet
Systematic Topology Analysis and Generation Using Degree Correlations
We present a new, systematic approach for analyzing network topologies. We
first introduce the dK-series of probability distributions specifying all
degree correlations within d-sized subgraphs of a given graph G. Increasing
values of d capture progressively more properties of G at the cost of more
complex representation of the probability distribution. Using this series, we
can quantitatively measure the distance between two graphs and construct random
graphs that accurately reproduce virtually all metrics proposed in the
literature. The nature of the dK-series implies that it will also capture any
future metrics that may be proposed. Using our approach, we construct graphs
for d=0,1,2,3 and demonstrate that these graphs reproduce, with increasing
accuracy, important properties of measured and modeled Internet topologies. We
find that the d=2 case is sufficient for most practical purposes, while d=3
essentially reconstructs the Internet AS- and router-level topologies exactly.
We hope that a systematic method to analyze and synthesize topologies offers a
significant improvement to the set of tools available to network topology and
protocol researchers.Comment: Final versio
Topological network alignment uncovers biological function and phylogeny
Sequence comparison and alignment has had an enormous impact on our
understanding of evolution, biology, and disease. Comparison and alignment of
biological networks will likely have a similar impact. Existing network
alignments use information external to the networks, such as sequence, because
no good algorithm for purely topological alignment has yet been devised. In
this paper, we present a novel algorithm based solely on network topology, that
can be used to align any two networks. We apply it to biological networks to
produce by far the most complete topological alignments of biological networks
to date. We demonstrate that both species phylogeny and detailed biological
function of individual proteins can be extracted from our alignments.
Topology-based alignments have the potential to provide a completely new,
independent source of phylogenetic information. Our alignment of the
protein-protein interaction networks of two very different species--yeast and
human--indicate that even distant species share a surprising amount of network
topology with each other, suggesting broad similarities in internal cellular
wiring across all life on Earth.Comment: Algorithm explained in more details. Additional analysis adde
Integration of molecular network data reconstructs Gene Ontology.
Motivation: Recently, a shift was made from using Gene Ontology (GO) to evaluate molecular network data to using these data to construct and evaluate GO. Dutkowski et al. provide the first evidence that a large part of GO can be reconstructed solely from topologies of molecular networks. Motivated by this work, we develop a novel data integration framework that integrates multiple types of molecular network data to reconstruct and update GO. We ask how much of GO can be recovered by integrating various molecular interaction data. Results: We introduce a computational framework for integration of various biological networks using penalized non-negative matrix tri-factorization (PNMTF). It takes all network data in a matrix form and performs simultaneous clustering of genes and GO terms, inducing new relations between genes and GO terms (annotations) and between GO terms themselves. To improve the accuracy of our predicted relations, we extend the integration methodology to include additional topological information represented as the similarity in wiring around non-interacting genes. Surprisingly, by integrating topologies of bakers’ yeasts protein–protein interaction, genetic interaction (GI) and co-expression networks, our method reports as related 96% of GO terms that are directly related in GO. The inclusion of the wiring similarity of non-interacting genes contributes 6% to this large GO term association capture. Furthermore, we use our method to infer new relationships between GO terms solely from the topologies of these networks and validate 44% of our predictions in the literature. In addition, our integration method reproduces 48% of cellular component, 41% of molecular function and 41% of biological process GO terms, outperforming the previous method in the former two domains of GO. Finally, we predict new GO annotations of yeast genes and validate our predictions through GIs profiling. Availability and implementation: Supplementary Tables of new GO term associations and predicted gene annotations are available at http://bio-nets.doc.ic.ac.uk/GO-Reconstruction/. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online
Semantic Object Parsing with Graph LSTM
By taking the semantic object parsing task as an exemplar application
scenario, we propose the Graph Long Short-Term Memory (Graph LSTM) network,
which is the generalization of LSTM from sequential data or multi-dimensional
data to general graph-structured data. Particularly, instead of evenly and
fixedly dividing an image to pixels or patches in existing multi-dimensional
LSTM structures (e.g., Row, Grid and Diagonal LSTMs), we take each
arbitrary-shaped superpixel as a semantically consistent node, and adaptively
construct an undirected graph for each image, where the spatial relations of
the superpixels are naturally used as edges. Constructed on such an adaptive
graph topology, the Graph LSTM is more naturally aligned with the visual
patterns in the image (e.g., object boundaries or appearance similarities) and
provides a more economical information propagation route. Furthermore, for each
optimization step over Graph LSTM, we propose to use a confidence-driven scheme
to update the hidden and memory states of nodes progressively till all nodes
are updated. In addition, for each node, the forgets gates are adaptively
learned to capture different degrees of semantic correlation with neighboring
nodes. Comprehensive evaluations on four diverse semantic object parsing
datasets well demonstrate the significant superiority of our Graph LSTM over
other state-of-the-art solutions.Comment: 18 page
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