Abstract
In order to compare biological networks numerous methods have been developed. Here, we give an overview of existing methods to compare biological networks meaningfully. Therefore we survey classical approaches of exact an inexact graph matching and discuss existing approaches to compare special types of biological networks. Moreover we review graph kernel-based methods and describe an approach based on structural network measures to classify large biological networks. The aim of this chapter is to provide a survey of techniques to compare biological networks for the interdisciplinary research community dealing with novel research questions in the field of systems biology
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- GED:
-
Graph Edit Distance
- GEO:
-
Gene Expression Omnibus
- GO:
-
Gene Ontology
- PPI:
-
Protein Protein Interactions
- QSAR:
-
Quantitative Structure-Activity Relationship
- QSPR:
-
Quantitative Structure-Property Relationships
References
Airola A, Pyysalo S, Björne J, Pahikkala T, Ginter F, Salakoski T (2008) A graph Kernel for protein-protein interaction extraction. In: Proceedings of the workshop on current trends in biomedical natural language processing, pp. 1–9. Association for, Computational Linguistics, 2008.
Airola A, Pyysalo S, Björne J, Pahikkala T, Ginter F, Salakoski T (2008) All-paths graph Kernel for protein-protein interaction extraction with evaluation of Cross-Corpus learning. BMC Bioinformatics 9(Suppl 11):S2
Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2007) Molecular biology of the cell. Garland Science, 5th edn
Altay G, Emmert Streib F (2010) Inferring the conservative causal core of gene regulatory networks. BMC Syst Biol 4(1):132
Altschul SF, Madden TL, Schäffer AA, Zhang J, Zhang Z, Miller W, Lipman DJ (1997) Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res 25(17):3389–3402
Ambroise C, McLachlan GJ (2002) Selection bias in gene extraction on the basis of microarray gene-expression data. Proc Nat Acad Sci USA 99(10):6562
Ay F, Dang M, Kahveci T (2012) Metabolic network alignment in large scale by network compression. BMC Bioinformatics 13(Suppl 3):S2
Ay F, Kahveci T (2010) SubMAP: aligning metabolic pathways with subnetwork mappings. In Research in computational molecular biology. Springer, New York, pp 15–30
Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 206:509–512
Basak SC, Magnuson VR, Niemi GJ, Regal RR (1988) Determining structural similarity of chemicals using graph-theoretic indices. Discrete Appl Math 19(1–3):17–44
Bhattacharyya A (1943) On a measure of divergence between two statistical populations defined by their probability distributions. Bull Calcutta Mathl Soc 35:99–109
Bonchev D (1983) Information theoretic indices for characterization of chemical structures. Chemometrics research studies series. Research Studies Press
Bonchev D, Mekenyan O, Trinajstić N (1981) Isomer discrimination by topological information approach. J Comput Chem 2(2):127–148
Bonchev D, Trinajstić N (1977) Information theory, distance matrix and molecular branching. J Chem Phys 67:4517–4533
Borgwardt KM, Kriegel HP (2005) Shortest-Path Kernels on graphs. In Data mining, Fifth IEEE International Conference on. IEEE, p 8
Borgwardt KM, Kriegel HP, Vishwanathan SVN, Schraudolph NN (2007) Graph Kernels for disease outcome prediction from Protein-Protein interaction networks, vol 12. In: Proceedings of Pacific symposium on biocomputing (PSB), pp 4–15
Borgwardt KM, Ong CS, Schönauer S, Vishwanathan SVN, Smola AJ, Kriegel HP (2005) Protein function prediction via graph Kernels. Bioinformatics 21(suppl 1):i47–i56
Breiman L (2001) Random Forests. Mach Learn 45(1):5–32
Bunke H (2000) Graph matching: theoretical foundations, algorithms, and applications. Proc Vis Interface 2000:82–88
Bunke H, Allermann G (1983) Inexact graph matching for structural pattern recognition. Pattern Recogn Lett 1(4):245–253
Bunke H, Riesen K (2009) Graph edit distance-optimal and suboptimal algorithms with applications. Anal Complex Netw pp 113–143
Cantrell CD (2000) Modern mathematical methods for physicists and engineers. Cambridge University Press, Cambridge
Chan AHS (2010) Advances in industrial engineering and operations research. Lecture notes in electrical engineering. Springer, New York
Conte D, Foggia P, Sansone C, Vento M (2004) Thirty years of graph matching in pattern recognition. Int J Pattern Recogn Artif Intell 18(3):265–298
Cordella LP, Foggia P, Sansone C, Vento M (1996) An efficient algorithm for the inexact matching of Arg Graphs using a contextual transformational model, vol 3. In: Proceedings of the 13th international conference on pattern recognition. IEEE, pp 180–184
Cordella LP, Foggia P, Sansone C, Vento M (2000) Fast graph matching for detecting CAD image components, vol 2. In: 15th international conference on pattern recognition. IEEE, pp 1034–1037
Cordella LP, Foggia P, Sansone C, Vento M (2001) An improved algorithm for matching large graphs. In: 3rd IAPR-TC15 workshop on graph-based representations in, pattern recognition, pp 149–159
Dankelmann P (2011) On the distance distribution of trees. Discrete Appl Math
Dehmer M, Barbarini N, Varmuza K, Graber A (2009) A large scale analysis of information-theoretic network complexity measures using chemical structures. PLoS ONE 4(12)
Dehmer M, Barbarini N, Varmuza K, Graber A (2010) Novel topological descriptors for analyzing biological networks. BMC Struct Biol 10(1):18
Dehmer M, Emmert Streib F (2007) Structural similarity of directed universal hierarchical graphs: a low computational complexity approach. Appl Math Comput 194(1):7–20
Dehmer M, Emmert Streib F, Tsoy YR, Varmuza K (2010) Quantum Frontiers of atoms and molecules, chapter quantifying structural complexity of graphs: information measures in mathematical. Nova, 2010
Dehmer M, Grabner M, Varmuza K (2012) Information indices with high discriminative power for graphs. PLoS ONE 7(2):e31214
Dehmer M, Mehler A (2007) A new method of measuring similarity for a special class of directed graphs. Tatra Mountains Math Publ 36:39–59
Dehmer M, Mowshowitz A (2011) A history of graph entropy measures. Inf Sci 181(1):57–78
Dehmer M, Sivakumar L, Varmuza K (2012) Uniquely discriminating molecular structures using novel eigenvalue based descriptors. MATCH Commun Math Comput Chem 67(1):147–172
Dodge CW (2004) Euclidean geometry and transformations. Dover Publications, New York
Dreyfus SE (1969) An appraisal of some shortest-path algorithms. Oper Res, pp 395–412
Edgar R, Domrachev M, Lash AE (2002) Gene expression omnibus: NCBI gene expression and hybridization array data repository. Nucleic Acids Res 30(1):207–210
Emmert Streib F (2007) The Chronic Fatigue syndrome: a comparative pathway analysis. J Computl Biol 14(7):961–972
Emmert Streib F, Dehmer M (May 2011) Networks for systems biology: conceptual connection of data and function. IET Syst Biol 5(3):185–207
Emmert Streib F, Dehmer M, Kilian J (2005) Classification of large graphs by a local tree decomposition. Proc DMIN 5:20–23
Emmert Streib F, Glazko GV (2010) Network biology: a direct approach to study biological function. Wiley Interdisciplinary Reviews. Systems biology and medicine, Dec 2010, pp 1–27
Eppstein D (1995). Subgraph Isomorphism in Planar Graphs and Related Problems. In Proceedings of the Sixth Annual ACM-SIAM symposium on discrete algorithms. Society for Industrial and, Applied Mathematics, pp. 632–640
Eshera MA, FU K (1984) A graph distance measure for image analysis. IEEE Trans Syst, Man, and Cybern 14(3):398–408
Eshera MA, Fu KS (1986) An image understanding system using attributed symbolic representation and inexact graph-matching. Pattern Anal Mach Intell IEEE Trans 5:604–618
Feng J, Lurati L, Ouyang H, Robinson T, Wang Y, Yuan S, Young SS (2003) Predictive toxicology: benchmarking molecular descriptors and statistical methods. J Chem Inf Comput Sci 43(5):1463–1470
Flannick J, Novak A, Srinivasan BS, McAdams HH, Batzoglou S (2006) Graemlin: General and robust alignment of multiple large interaction networks. Genome Res 16(9):1169–1181
Gärtner T, Flach P, Wrobel S (2003) On graph Kernels: hardness results and efficient alternatives. Learn Theory Kernel Mach, pp 129–143
Guzmn Vargas L, Santilln M (2008) Comparative analysis of the transcription-factor gene regulatory networks of E. Coli and S. Cerevisiae. BMC Syst Biol 2:13
Hansen K, Mika S, Schroeter T, Sutter A, Ter Laak A, Steger Hartmann T, Heinrich N, Muller KR (2009) Benchmark data set for in Silico prediction of Ames mutagenicity. J Chem Inf Comput Sci 49(9):2077–2081
Harary F (1994) Graph theory. Perseus Books, Addison-Wesley, New York, Reading
Harris MA, Clark J, Ireland A, Lomax J, Ashburner M, Foulger R et al (2004) The Gene Ontology (GO) database and informatics resource. Nucleic Acids Res 32(Database issue):D258
Hart PE, Nilsson NJ, Raphael B (1968) A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Syst Sci Cybern 4(2):100–107
Helma C, Cramer T, Kramer S, De Raedt L (2004) Data mining and machine learning techniques for the identification of mutagenicity inducing substructures and structure activity relationships of noncongeneric compounds. J Chem Inf Comput Sci 44(4):1402–1411
Hood L, Heath JR, Phelps ME, Lin B (2004) Systems biology and new technologies enable predictive and preventative medicine. Science 306(5696):640
Horváth T (2005) Cyclic pattern Kernels revisited. Adv Knowl Discov Data Min, pp 139–140
Horváth T, Gärtner T, Wrobel S (2004) Cyclic pattern Kernels for predictive graph mining. In: Proceedings of the Tenth ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 158–167
Jeong H, Tombor B, Albert R, Oltvai ZN, Barabsi AL (Oct 2000) The large-scale organization of metabolic networks. Nature 407(6804):651–654
Kalaev M, Smoot M, Ideker T, Sharan R (2008) NetworkBLAST: comparative analysis of protein networks. Bioinformatics 24(4):594–596
Kashima H, Inokuchi A (2002) Kernels for graph classification, vol 2002. In: ICDM workshop on active mining, p 25
Kelley BP, Sharan R, Karp RM, Sittler T, Root DE, Stockwell BR, Ideker T (2003) Conserved pathways within Bacteria and Yeast as revealed by global protein network alignment. Sci STKE 100(20):11394
Kelley BP, Yuan B, Lewitter F, Sharan R, Stockwell BR, Ideker T (2004) PathBLAST: a tool for alignment of Protein interaction networks. Nucleic Acids Res 32(suppl 2):W83–W88
Kitano H (2002) Systems biology: a brief overview. Science 295:1662–1664
Koyutürk M, Grama A, Szpankowski W (2005) Pairwise local alignment of Protein interaction networks guided by models of evolution. In: Research in computational molecular biology. Springer, New York, pp 995–995
Koyutürk M, Kim Y, Topkara U, Subramaniam S, Szpankowski W, Grama A (2006) Pairwise alignment of protein interaction networks. J Comput Biol 13(2):182–199
Krause EF (1973) Taxicab geometry. Math Teach 66(8):695–706
Kuchaiev O, Milenković T, Memišević V, Hayes W, Pržulj N (2010) Topological network alignment uncovers biological function and phylogeny. J Royal Soc Interf 7(50):1341–1354
Kuchaiev O, Pržulj N (2011) Integrative network alignment reveals large regions of global network similarity in Yeast and Human. Bioinformatics 27(10):1390–1396
Kugler KG, Mueller LAJ, Graber A, Dehmer M (2011) Integrative network biology: graph prototyping for co-expression cancer networks. PLoS ONE 6(7):e22843
Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79–86
Lance GN, Williams WT (1966) Computer programs for hierarchical polythetic classification (similarity analyses). Comput J 9(1):60–64
Langfelder P, Horvath S (January 2008) WGCNA: an R package for weighted correlation network analysis. BMC Bioinformatics 9:559
Larrosa J, Valiente G (2002) Constraint satisfaction algorithms for graph pattern matching. Math Struct Comput Sci 12(4):403–422
Liao CS, Lu K, Baym M, Singh R, Berger B (2009) IsoRankN: spectral methods for global alignment of multiple protein networks. Bioinformatics 25(12):i253–i258
Liu H, Motoda H (1998) Feature selection for knowledge discovery and data mining. Kluwer Academic Publishers, Dordrecht
Mahé P, Vert JP (2009) Graph Kernels based on tree patterns for molecules. Mach Learn 75(1):3–35
Mazurie A, Bonchev D, Schwikowski B, Buck GA (2008) Phylogenetic distances are encoded in networks of interacting pathways. Bioinformatics 24(22):2579
McKay BD Nauty. http://cs.anu.edu.au/ bdm/nauty/
McKay BD (1981) Practical graph isomorphism. Congressus Numerantium 30:45–87
Menchetti S, Costa F, Frasconi P (2005) Weighted decomposition Kernels. In: Proceedings of the 22nd international conference on machine learning. ACM, pp 585–592
Messmer BT, Bunke H (1999) A decision tree approach to graph and subgraph isomorphism detection. Pattern Recogn 32(12):1979–1998
Messmer BT, Bunke H (2000) Efficient subgraph isomorphism detection: a decomposition approach. IEEE Trans Knowl Data Eng 12(2):307–323
Meyer PE, Kontos K, Lafitte F, Bontempi G (2007) Information-theoretic inference of large transcriptional regulatory networks. EURASIP J Bioinform Syst Biol 8–8:2007
Michoel T, De Smet R, Joshi A, Van de Peer Y, Marchal K (2009) Comparative analysis of module-based versus direct methods for reverse-engineering transcriptional regulatory networks. BMC Syst Biol 3(1):49
Milenkoviæ T, Pržulj N (2008) Uncovering biological network function via Graphlet degree signatures. Cancer Inform 6:257
Mowshowitz A (1968) Entropy and the complexity of the graphs I: an index of the relative complexity of a graph. Bull Math Biophys 30:175204
Mueller LAJ, Kugler KG, Dander A, Graber A, Dehmer M (2010) Network-based approach to classify disease stages of prostate cancer using quantitative network measures, vol I. Conference on bioinformatics and computational biology (BIOCOMP’10), Las Vegas/USA, pp 55–61
Mueller LAJ, Kugler KG, Dander A, Graber A, Dehmer M (2011) QuACN: an R package for analyzing complex biological networks quantitatively. Bioinformatics 27(1):140
Mueller LAJ, Kugler KG, Graber A, Emmert Streib F, Dehmer M (2011) Structural measures for network biology using QuACN. BMC Bioinformatics 12(1):492
Mueller LAJ, Kugler KG, Netzer M, Graber A, Dehmer M (2011) A network-based approach to classify the three domains of life. Biology Direct 6(1):53
Neuhaus M, Riesen K, Bunke H (2006) Fast suboptimal algorithms for the computation of graph edit distance. In: Structural, syntactic, and statistical, pattern recognition, pp 163–172
Palsson B (2006) Systems biology: properties of reconstructed networks. Cambridge University Press, Cambridge
Parkinson H, Kapushesky M, Kolesnikov N, Rustici G, Shojatalab M, Abeygunawardena N, Berube H, Dylag M, Emam I, Farne A et al (2009) ArrayExpress update from an archive of functional genomics experiments to the Atlas of gene expression. Nucleic Acids Res 37(suppl 1):D868–D872
Passerini F, Severini S (2009) Quantifying complexity in networks: the von Neumann entropy. Int J Agent Technol Syst (IJATS) 1(4):58–67
Poston KL, Eidelberg D (2009) Network biomarkers for the diagnosis and treatment of movement disorders. Neurobiol Dis 35(2):141–147
Pržulj N (2007) Biological network comparison using graphlet degree distribution. Bioinformatics 23(2):e177–e183
Ralaivola L, Swamidass SJ, Saigo H, Baldi P (2005) Graph kernels for chemical informatics. Neural Networks 18(8):1093–1110
Riesen K, Bunke H (2009) Approximate graph edit distance computation by means of bipartite graph matching. Image Vis Comput 27(7):950–959
Ruan J, Dean AK, Zhang W (2010) A general co-expression network-based approach to gene expression analysis: comparison and applications. BMC Syst Biol 4(1):8
Rudolf M (2000) Utilizing constraint satisfaction techniques for efficient graph pattern matching. Theory Appl Graph Transform, pp 381–394
Rupp M, Schneider G (2010) Graph Kernels for molecular similarity. Mol Inform 29(4):266–273
Rupp M, Schneider P, Schneider G (2009) Distance phenomena in high-dimensional chemical descriptor spaces: consequences for similarity-based approaches. J Comput Chem 30(14):2285–2296
Sanfeliu A, King Sun F (1983) A distance measure between attributed relational graphs for pattern recognition. IEEE Trans Syst Man Cybern 13(3):353–362
Schölkopf B, Tsuda K, Vert JP (2004) Kernel methods in computational biology. Computational molecular biology. MIT Press, Cambridge
Scsibrany H, Karlovits M, Demuth W, Müller F, Varmuza K (2003) Clustering and similarity of chemical structures represented by binary substructure descriptors. Chemometr Intell Lab Syst 67(2):95–108
Serratosa F, Alquézar R, Sanfeliu A (2003) Function-described graphs for modelling objects represented by sets of attributed graphs. Pattern Recogn 36(3):781–798
Shapiro LG, Haralick RM (1981) Structural descriptions and inexact graph matching. IEEE Trans Pattern Anal Mach Intell 3:504–519
Sharan R, Ideker T (2006) Modeling cellular machinery through biological network comparison. Nat Biotechnol 24(4):427–433
Sharan R, Suthram S, Kelley RM, Kuhn T, McCuine S, Uetz P, Sittler T, Karp RM, Ideker T (2005) Conserved patterns of Protein interaction in multiple species. Proc Natl Acad Sci USA 102(6):1974
Shervashidze N, Borgwardt KM (2009) Fast subtree Kernels on graphs. Adv Neural Inf Proc Syst 22:1660–1668
Shervashidze N, Vishwanathan SVN, Petri T, Mehlhorn K, Borgwardt K (2009) Efficient graphlet Kernels for large graph comparison. In: Proceedings of the international workshop on artificial intelligence and statistics. Society for Artificial Intelligence and, Statistics, 2009
Shih YK, Parthasarathy S (2012) Scalable global alignment for multiple biological networks. BMC Bioinformatics 13(Suppl 3):S11
Singh R, Xu J, Berger B (2007) Pairwise global alignment of Protein interaction networks by matching neighborhood topology. In: Research in computational molecular biology. Springer, New York, pp 16–31
Singh R, Xu J, Berger B (2008) Global alignment of multiple Protein interaction networks with application to functional orthology detection. Proc Natl Acad Sci 105(35):12763
Smialowski P, Frishman D, Kramer S (2010) Pitfalls of supervised feature selection. Bioinformatics 26(3):440
Sobik F (1982) Graphmetriken und Klassifikation strukturierter Objekte. ZKI-Inf, Akad Wiss DDR 2:63–122
Todeschini R, Mannhold R (2002) Handbook of molecular descriptors. Wiley-VCH, Weinheim, Germany
Tsai WH, Fu KS (1979) Error-correcting isomorphisms of attributed relational graphs for pattern analysis. IEEE Trans Syst, Man Cybern 9(12):757–768
Tsai WH, Fu KS (1983) Subgraph error-correcting isomorphisms for syntactic pattern recognition. IEEE Trans Syst, Man Cybern 13(1):48–62
Ullmann JR (1976) An algorithm for subgraph isomorphism. J ACM (JACM) 23(1):31–42
Vapnik VN (2000) The nature of statistical learning theory. Springer, New York
Wang J, Provan G (2009) Characterizing the structural complexity of real-world complex networks. Complex Sci, pp 1178–1189
Watts DJ, Strogatz SH (1998) Collective dynamics of ’Small-world’ networks. Nature 393:440–442
Wong EK (1990) Three-dimensional object recognition by attributed graphs. Syntactic Struct Pattern Recogn Theory Appl, pp 381–414
Xia K, Fu Z, Hou L, Han JDJ (2008) Impacts of Protein-Protein interaction domains on organism and network complexity. Genome Res 18(9):1500
Zaslavskiy M, Bach F, Vert JP (2009) Global alignment of Protein-Protein interaction networks by graph matching methods. Bioinformatics 25(12):i259–1267
Zelinka A (1975) On a certain distance between isomorphism classes of graphs. Čas Pěst Mat 100:371375
Acknowledgments
This work was supported by the Tiroler Wissenschaftsfonds and the Standortagentur Tirol (formerly Tiroler Zukunftsstiftung).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Mueller, L.A.J., Dehmer, M., Emmert-Streib, F. (2013). Comparing Biological Networks: A Survey on Graph Classifying Techniques. In: Prokop, A., Csukás, B. (eds) Systems Biology. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6803-1_2
Download citation
DOI: https://doi.org/10.1007/978-94-007-6803-1_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-6802-4
Online ISBN: 978-94-007-6803-1
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)