99,809 research outputs found
Graph measures and network robustness
Network robustness research aims at finding a measure to quantify network
robustness. Once such a measure has been established, we will be able to
compare networks, to improve existing networks and to design new networks that
are able to continue to perform well when it is subject to failures or attacks.
In this paper we survey a large amount of robustness measures on simple,
undirected and unweighted graphs, in order to offer a tool for network
administrators to evaluate and improve the robustness of their network. The
measures discussed in this paper are based on the concepts of connectivity
(including reliability polynomials), distance, betweenness and clustering. Some
other measures are notions from spectral graph theory, more precisely, they are
functions of the Laplacian eigenvalues. In addition to surveying these graph
measures, the paper also contains a discussion of their functionality as a
measure for topological network robustness
Exploring Robustness of Neural Networks through Graph Measures
Motivated by graph theory, artificial neural networks (ANNs) are
traditionally structured as layers of neurons (nodes), which learn useful
information by the passage of data through interconnections (edges). In the
machine learning realm, graph structures (i.e., neurons and connections) of
ANNs have recently been explored using various graph-theoretic measures linked
to their predictive performance. On the other hand, in network science
(NetSci), certain graph measures including entropy and curvature are known to
provide insight into the robustness and fragility of real-world networks. In
this work, we use these graph measures to explore the robustness of various
ANNs to adversarial attacks. To this end, we (1) explore the design space of
inter-layer and intra-layers connectivity regimes of ANNs in the graph domain
and record their predictive performance after training under different types of
adversarial attacks, (2) use graph representations for both inter-layer and
intra-layers connectivity regimes to calculate various graph-theoretic
measures, including curvature and entropy, and (3) analyze the relationship
between these graph measures and the adversarial performance of ANNs. We show
that curvature and entropy, while operating in the graph domain, can quantify
the robustness of ANNs without having to train these ANNs. Our results suggest
that the real-world networks, including brain networks, financial networks, and
social networks may provide important clues to the neural architecture search
for robust ANNs. We propose a search strategy that efficiently finds robust
ANNs amongst a set of well-performing ANNs without having a need to train all
of these ANNs.Comment: 18 pages, 15 figure
Robustness in Nonorthogonal Multiple Access 5G Networks
The diversity of fifth generation (5G) network use cases, multiple access technologies, and network deployments requires measures of network robustness that complement throughput-centric error rates. In this paper, we investigate robustness in nonorthogonal multiple access (NOMA) 5G networks through temporal network theory. We develop a graph model and analytical framework to characterize time-varying network connectedness as a function of NOMA overloading. We extend our analysis to derive lower bounds and probability expressions for the number of medium access control frames required to achieve pairwise connectivity between all network devices. We support our analytical results through simulation
Characterizing Distances of Networks on the Tensor Manifold
At the core of understanding dynamical systems is the ability to maintain and
control the systems behavior that includes notions of robustness,
heterogeneity, or regime-shift detection. Recently, to explore such functional
properties, a convenient representation has been to model such dynamical
systems as a weighted graph consisting of a finite, but very large number of
interacting agents. This said, there exists very limited relevant statistical
theory that is able cope with real-life data, i.e., how does perform analysis
and/or statistics over a family of networks as opposed to a specific network or
network-to-network variation. Here, we are interested in the analysis of
network families whereby each network represents a point on an underlying
statistical manifold. To do so, we explore the Riemannian structure of the
tensor manifold developed by Pennec previously applied to Diffusion Tensor
Imaging (DTI) towards the problem of network analysis. In particular, while
this note focuses on Pennec definition of geodesics amongst a family of
networks, we show how it lays the foundation for future work for developing
measures of network robustness for regime-shift detection. We conclude with
experiments highlighting the proposed distance on synthetic networks and an
application towards biological (stem-cell) systems.Comment: This paper is accepted at 8th International Conference on Complex
Networks 201
Closeness centrality in some splitting networks
A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A variety of measures have been proposed in the literature to quantify the robustness of networks, and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. \textit{Centrality} parameters play an important role in the field of network analysis. Numerous studies have proposed and analyzed several \textit{centrality} measures. We consider \textit{closeness centrality} which is defined as the total graph-theoretic distance to all other vertices in the graph. In this paper, closeness centrality of some splitting graphs is calculated, and exact values are obtained
Graph-theoretical comparison of normal and tumor networks in identifying BRCA genes
Background: Identification of driver genes related to certain types of cancer is an important research topic. Several systems biology approaches have been suggested, in particular for the identification of breast cancer (BRCA) related genes. Such approaches usually rely on differential gene expression and/or mutational landscape data. In some cases interaction network data is also integrated to identify cancer-related modules computationally.
Results: We provide a framework for the comparative graph-theoretical analysis of networks integrating the relevant gene expression, mutations, and potein-protein interaction network data. The comparisons involve a
graph-theoretical analysis of normal and tumor network pairs across all instances of a given set of breast cancer samples. The network measures under consideration are based on appropriate formulations of various centrality measures: betweenness, clustering coefficients, degree centrality, random walk distances, graph-theoretical distances, and Jaccard index centrality.
Conclusions: Among all the studied centrality-based graph-theoretical properties, we show that a betweenness-based measure differentiates BRCA genes across all normal versus tumor network pairs, than the rest of the popular centrality-based measures. The AUROC and AUPR values of the gene lists ordered with respect to the measures under study as compared to NCBI BioSystems pathway and the COSMIC database of cancer genes are the largest with the betweenness-based differentiation, followed by the measure based on degree centrality. In order to test the robustness of the suggested measures in prioritizing cancer genes, we further tested the two most promising measures, those based on betweenness and degree centralities, on randomly rewired networks. We show that both measures are quite resilient to noise in the input interaction network. We also compared the same measures against a
state-of-the-art alternative disease gene prioritization method, UFFFINN. We show that both our graph-theoretical measures outperform MUFFINN prioritizations in terms of ROC and precions/recall analysis. Finally, we filter the ordered list of the best measure, the betweenness-based differentiation, via a maximum-weight independent set formulation and investigate the top 50 genes in regards to literature verification. We show that almost all genes in the list are verified by the breast cancer literature and three genes are presented as novel genes that may potentialy be
BRCA-related but missing in literature.No sponso
Super edge-connectivity and matching preclusion of data center networks
Edge-connectivity is a classic measure for reliability of a network in the
presence of edge failures. -restricted edge-connectivity is one of the
refined indicators for fault tolerance of large networks. Matching preclusion
and conditional matching preclusion are two important measures for the
robustness of networks in edge fault scenario. In this paper, we show that the
DCell network is super- for and ,
super- for and , or and , and
super- for and . Moreover, as an application of
-restricted edge-connectivity, we study the matching preclusion number and
conditional matching preclusion number, and characterize the corresponding
optimal solutions of . In particular, we have shown that is
isomorphic to the -star graph for .Comment: 20 pages, 1 figur
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