Network Properties Revealed through Matrix Functions

Estrada, Ernesto; Higham, Desmond J.

doi:10.1137/090761070

Cited by 280 publications

(271 citation statements)

References 59 publications

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“…which eventually converges to the trace of the resolvent of the adjacency matrix (Estrada and Higham, 2008),…”

Section: Preliminary Definitionsmentioning

confidence: 90%

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Generalized walks-based centrality measures for complex biological networks

Estrada

2010

Journal of Theoretical Biology

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A strategy for zooming in and out the topological environment of a node in a complex network is developed. This approach is applied here to generalize the subgraph centrality of nodes in complex networks. In this case the zooming in strategy is based on the use of some known matrix functions which allow focusing locally on the environment of a node. When a zooming out strategy is applied new matrix functions are introduced, which give a more global picture of the topological surrounds of a node. These indices permit a modulation of the scales at which the environment of a node influences its centrality. We apply them to the study of 10 protein-protein interaction (PPI) networks. We illustrate the similarities and differences between the generalized subgraph centrality indices as well as among them and some classical centrality measures. We show here that the use of centrality indices based on the zooming in strategy identifies a larger number of essential proteins in the yeast PPI network than any of the other centrality measures studied.

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“…which eventually converges to the trace of the resolvent of the adjacency matrix (Estrada and Higham, 2008),…”

Section: Preliminary Definitionsmentioning

confidence: 90%

“…Recently Estrada and Higham (2008) proposed a general formulation for the invariants based on Taylor series expansion of spectral moments…”

Section: Preliminary Definitionsmentioning

confidence: 99%

Generalized walks-based centrality measures for complex biological networks

Estrada

2010

Journal of Theoretical Biology

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“…The general concepts, such as centrality, communicability and betweenness, quantify the important features in a network (34). Estrada (35) demonstrated that subgraph centrality could be applied to the identification of essential proteins in PPI networks.…”

Section: Discussionmentioning

confidence: 99%

Identification of the potential molecular targets for human intervertebral disc degeneration based on bioinformatic methods

Xue

Liu

et al. 2015

International Journal of Molecular Medicine

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Abstract. The present study aimed to explore potential molecular targets and gain further insights into the mechanism of intervertebral disc degeneration (IDD) progression. Microarray datasets of GSE19943, GSE15227 and GSE34095 were downloaded from the Gene Expression Omnibus database. Differentially expressed genes (DEGs) in 3 IDD specimens compared with 3 controls in GSE34095, DEGs in 7 grade III and 3 grade IV samples compared with 5 grade II samples in GSE19943, and differentially expressed miRNAs in 3 degenerated samples compared with 3 controls in GSE15227 were screened. Grade III-and IV-specific networks were constructed and grade-specific genes were extracted. The network features were analyzed, followed by Gene Ontology (GO) enrichment analysis and pathway enrichment analysis of grade-specific genes and DEGs identified in GSE34095. Furthermore, miRNA-pathway interactions were analyzed using Fisher's exact test. Tumor protein p53 (TP53) was a hub gene in the grade III-specific network and ubiquitin C (UBC) was identified to be a hub gene in the grade IV-specific network. Six significant features were identified by grade-specific network topology analysis. Grade-specific genes and DEGs were involved in different GO terms and pathways. Differentially expressed miRNAs were identified to participate in 35 pathways, among which 6 pathways were significantly enriched by DEGs, including apoptosis. The present study identified that key genes (TP53 and UBC) and miR-129-5p may participate in the mechanism of IDD progression. Thus, they may be potential therapeutic targets for IDD.

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“…The walk viewpoint is also in line with the influential work of Katz [17] for the study of static, undirected social networks. The explicit use of a walk based measure of centrality was proposed for the static case in [9], and the idea has been shown to lead to very powerful measures that are useful across a range of application areas [6,10,11]. A further benefit of the walk counting approach is that the combinatorics can be conveniently described and implemented in terms of operations in linear algebra, and we will show that this feature can be carried through to the dynamic case.…”

Section: Dynamic Centralitiesmentioning

confidence: 95%

Communicability across evolving networks

et al. 2011

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Many natural and technological applications generate time-ordered sequences of networks, defined over a fixed set of nodes; for example, time-stamped information about “who phoned who” or “who came into contact with who” arise naturally in studies of communication and the spread of disease. Concepts and algorithms for static networks do not immediately carry through to this dynamic setting. For example, suppose A and B interact in the morning, and then B and C interact in the afternoon. Information, or disease, may then pass from A to C, but not vice versa. This subtlety is lost if we simply summarize using the daily aggregate network given by the chain A-B-C. However, using a natural definition of a walk on an evolving network, we show that classic centrality measures from the static setting can be extended in a computationally convenient manner. In particular, communicability indices can be computed to summarize the ability of each node to broadcast and receive information. The computations involve basic operations in linear algebra, and the asymmetry caused by time’s arrow is captured naturally through the noncommutativity of matrix-matrix multiplication. Illustrative examples are given for both synthetic and real-world communication data sets. We also discuss the use of the new centrality measures for real-time monitoring and prediction

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Network Properties Revealed through Matrix Functions

Cited by 280 publications

References 59 publications

Generalized walks-based centrality measures for complex biological networks

Generalized walks-based centrality measures for complex biological networks

Identification of the potential molecular targets for human intervertebral disc degeneration based on bioinformatic methods

Communicability across evolving networks

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