Skip to main content

Networks and Fundamental Concepts

Abstract

This chapter introduces basic terminology and network concepts. Subsequent chapters illustrate that many data analysis tasks can be addressed using network methods. Network concepts (also known as network statistics or network indices) can be used to describe the topological properties of a single network and for comparing two or more networks (e.g., differential network analysis). Dozens of potentially useful network concepts are known from graph theory, e.g., the connectivity, density, centralization, and topological overlap. Measures of node interconnectedness, e.g., based on generalizations of the topological overlap matrix, can be used in neighborhood analysis. We distinguish three types of fundamental network concepts: (1) whole network concepts are defined without reference to modules, (2) intramodular concepts describe network properties of a module, and (3) intermodular concepts describe relationships between two or more modules. Intermodular network concepts can be used to define networks whose nodes are modules.

Keywords

  • Adjacency Matrix
  • Cluster Coefficient
  • Node Significance
  • Network Concept
  • Neighborhood Analysis

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-1-4419-8819-5_1
  • Chapter length: 34 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   169.00
Price excludes VAT (USA)
  • ISBN: 978-1-4419-8819-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   219.99
Price excludes VAT (USA)
Hardcover Book
USD   299.99
Price excludes VAT (USA)
Fig. 1.1
Fig. 1.2
Fig. 1.3
Fig. 1.4
Fig. 1.5

References

  • Albert R, Barabasi AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97

    CrossRef  Google Scholar 

  • Albert R, Barabasi AL (2000) Topology of evolving networks: Local events and universality. Phys Rev Lett 85(24):5234–5237

    PubMed  CrossRef  CAS  Google Scholar 

  • Albert R, Jeong H, Barabasi AL (2000) Error and attack tolerance of complex networks. Nature 406(6794):378–382

    PubMed  CrossRef  CAS  Google Scholar 

  • Almaas E, Kovacs B, Vicsek T, Oltvai ZN, Barabasi AL (2004) Global organization of metabolic fluxes in the bacterium Escherichia coli. Nature 427:839–843

    PubMed  CrossRef  CAS  Google Scholar 

  • Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512

    PubMed  CrossRef  Google Scholar 

  • Barabasi AL, Oltvai ZN (2004) Network biology: Understanding the cell’s functional organization. Nat Rev Genet 5(2):101–113

    PubMed  CrossRef  CAS  Google Scholar 

  • Brun C, Chevenet F, Martin D, Wojcik J, Guenoche A, Jacq B (2003) Functional classification of proteins for the prediction of cellular function from a protein-protein interaction network. Genome Biol 5(1):R6

    PubMed  CrossRef  Google Scholar 

  • Carlson M, Zhang B, Fang Z, Mischel P, Horvath S, Nelson SF (2006) Gene connectivity, function, and sequence conservation: Predictions from modular yeast co-expression networks. BMC Genomics 7(7):40

    PubMed  CrossRef  Google Scholar 

  • Carter SL, Brechbuler CM, Griffin M, Bond AT (2004) Gene co-expression network topology provides a framework for molecular characterization of cellular state. Bioinformatics 20(14):2242–2250

    PubMed  CrossRef  CAS  Google Scholar 

  • Chen J, Hsu W, Lee ML, Ng S (2006) Increasing confidence of protein interactomes using network topological metrics. Bioinformatics 22:1998–2004

    PubMed  CrossRef  CAS  Google Scholar 

  • Chua NH, Sung W, Wong L (2006) Exploiting indirect neighbours and topological weight to predict protein function from proteinprotein interactions. Bioinformatics 22:1623–1630

    PubMed  CrossRef  CAS  Google Scholar 

  • Csanyi G, Szendroi B (2004) Structure of a large social network. Phys Rev 69:1–5

    Google Scholar 

  • Dong J, Horvath S (2007) Understanding network concepts in modules. BMC Syst Biol 1(1):24

    PubMed  CrossRef  Google Scholar 

  • Freeman L (1978) Centrality in social networks: Conceptual clarification. Soc Networks 1:215–239

    CrossRef  Google Scholar 

  • Fuller TF, Ghazalpour A, Aten JE, Drake T, Lusis AJ, Horvath S (2007) Weighted gene coexpression network analysis strategies applied to mouse weight. Mamm Genome 18(6–7):463–472

    PubMed  CrossRef  Google Scholar 

  • Gargalovic PS, Imura M, Zhang B, Gharavi NM, Clark MJ, Pagnon J, Yang WP, He A, Truong A, Patel S, Nelson SF, Horvath S, Berliner JA, Kirchgessner TG, Lusis AJ (2006) Identification of inflammatory gene modules based on variations of human endothelial cell responses to oxidized lipids. Proc Natl Acad Sci USA 103(34):12741–12746

    PubMed  CrossRef  CAS  Google Scholar 

  • Ghazalpour A, Doss S, Zhang B, Plaisier C, Wang S, Schadt EE, Thomas A, Drake TA, Lusis AJ, Horvath S (2006) Integrating genetics and network analysis to characterize genes related to mouse weight. PloS Genet 2(2):8

    CrossRef  Google Scholar 

  • Guldener U, Munsterkotter M, Oesterheld M, Pagel P, Ruepp A, Mewes HW, Stumpflen V (2006) MPact: The MIPS protein interaction resource on yeast. Nucleic Acids Res 34:436–441

    CrossRef  Google Scholar 

  • Hahn MW, Kern AD (2005) Comparative genomics of centrality and essentiality in three eukaryotic protein-interaction networks. Mol Biol Evol 22(4):803–806

    PubMed  CrossRef  CAS  Google Scholar 

  • Han JD, Bertin N, Hao T, Goldberg DS, Berriz GF, Zhang LV, Dupuy D, Walhout AJ, Cusick ME, Roth FP, Vidal M (2004) Evidence for dynamically organized modularity in the yeast protein-protein interaction network. Nature 430(6995):88–93

    PubMed  CrossRef  CAS  Google Scholar 

  • Horvath S, Dong J (2008) Geometric interpretation of gene co-expression network analysis. PLoS Comput Biol 4(8):e1000117

    PubMed  CrossRef  Google Scholar 

  • Horvath S, Zhang B, Carlson M, Lu KV, Zhu S, Felciano RM, Laurance MF, Zhao W, Shu Q, Lee Y, Scheck AC, Liau LM, Wu H, Geschwind DH, Febbo PG, Kornblum HI, Cloughesy TF, Nelson SF, Mischel PS (2006) Analysis of oncogenic signaling networks in glioblastoma identifies ASPM as a novel molecular target. Proc Natl Acad Sci USA 103(46):17402–17407

    PubMed  CrossRef  CAS  Google Scholar 

  • Jeong H, Mason SP, Barabasi AL, Oltvai ZN (2001) Lethality and centrality in protein networks. Nature 411:41

    PubMed  CrossRef  CAS  Google Scholar 

  • Jeong H, Oltvai Z, Barabasi A (2003) Prediction of protein essentiality based on genome data. ComPlexUs 1:19–28

    CrossRef  Google Scholar 

  • Kaufman L, Rousseeuw PJ (1990) Finding groups in data: An introduction to cluster analysis. Wiley, New York

    CrossRef  Google Scholar 

  • Li A, Horvath S (2007) Network neighborhood analysis with the multi-node topological overlap measure. Bioinformatics 23(2):222–231

    PubMed  CrossRef  Google Scholar 

  • Ma HW, Buer J, Zeng AP (2004) Hierarchical structure and modules in the Escherichia coli transcriptional regulatory network revealed by a new top-down approach. BMC Bioinform 5(1):199

    CrossRef  Google Scholar 

  • van Nas A, GuhaThakurta D, Wang SS, Yehya N, Horvath S, Zhang B, Ingram-Drake L, Chaudhuri G, Schadt EE, Drake TA, Arnold AP, Lusis AJ (2009) Elucidating the role of gonadal hormones in sexually dimorphic gene coexpression networks. Endocrinology 150(3):1235–1249

    PubMed  Google Scholar 

  • Oldham MC, Horvath S, Geschwind DH (2006) Conservation and evolution of gene coexpression networks in human and chimpanzee brains. Proc Natl Acad Sci USA 103(47):17973–17978

    PubMed  CrossRef  CAS  Google Scholar 

  • Oldham MC, Konopka G, Iwamoto K, Langfelder P, Kato T, Horvath S, Geschwind DH (2008) Functional organization of the transcriptome in human brain. Nat Neurosci 11(11):1271–1282

    PubMed  CrossRef  CAS  Google Scholar 

  • Pagel M, Meade A, Scott D (2007) Assembly rules for protein networks derived from phylogenetic-statistical analysis of whole genomes. BMC Evol Biol 7(Suppl 1):S16

    PubMed  CrossRef  Google Scholar 

  • Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabasi AL (2002) Hierarchical organization of modularity in metabolic networks. Science 297(5586):1551–1555

    PubMed  CrossRef  CAS  Google Scholar 

  • Snijders TA (1981) The degree variance: An index of graph heterogeneity. Soc Networks 3:163–174

    CrossRef  Google Scholar 

  • Swindell W (2007) Gene expression profiling of long-lived dwarf mice: Longevity-associated genes and relationships with diet, gender and aging. BMC Genomics 8(1):353

    PubMed  CrossRef  Google Scholar 

  • Watts DJ (2002) A simple model of global cascades on random networks. Proc Natl Acad Sci USA 99(9):5766–5771

    PubMed  CrossRef  CAS  Google Scholar 

  • Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393 (6684):440–442

    PubMed  CrossRef  CAS  Google Scholar 

  • Yip A, Horvath S (2007) Gene network interconnectedness and the generalized topological overlap measure. BMC Bioinform 8(8):22

    CrossRef  Google Scholar 

  • Zhang B, Horvath S (2005) General framework for weighted gene coexpression analysis. Stat Appl Genet Mol Biol 4:17

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Steve Horvath .

Rights and permissions

Reprints and Permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Horvath, S. (2011). Networks and Fundamental Concepts. In: Weighted Network Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8819-5_1

Download citation