Abstract.
Biological networks, such as cellular metabolic pathways or networks of corticocortical connections in the brain, are intricately organized, yet remarkably robust toward structural damage. Whereas many studies have investigated specific aspects of robustness, such as molecular mechanisms of repair, this article focuses more generally on how local structural features in networks may give rise to their global stability. In many networks the failure of single connections may be more likely than the extinction of entire nodes, yet no analysis of edge importance (edge vulnerability) has been provided so far for biological networks. We tested several measures for identifying vulnerable edges and compared their prediction performance in biological and artificial networks. Among the tested measures, edge frequency in all shortest paths of a network yielded a particularly high correlation with vulnerability and identified intercluster connections in biological but not in random and scale-free benchmark networks. We discuss different local and global network patterns and the edge vulnerability resulting from them.
Similar content being viewed by others
References
Albert R, Jeong H, Barabási A-L (2000) Error and attack tolerance of complex networks. Nature 406: 378–382
Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286: 509–512
Barabási A-L, Ravasz E, Vicsek T (2001) Deterministic scale-free networks. Physica A 3–4: 559–564
Büchel C, Friston KJ (1997) Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI. Cereb Cortex 7: 768–778
Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to Algorithms. MIT Press, Cambridge, MA
Damier P, Hirsch EC, Agid Y, Graybiel AM (1999) The substantia nigra of the human brain: II. Patterns of loss of dopamine-containing neurons in Parkinson’s disease. Brain 122: 1437–1448
Felleman DJ, van Essen DC (1991) Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1: 1–47
Gavin et al (2002) Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature 415: 141–147
Geschwind N (1965) Disconnection syndromes in animals and man: Part I. Brain 88: 229–237
Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99: 7821–7826
Granovetter MS (1973) The strength of weak ties. Am J Sociol 78: 1360–1380
Hilgetag CC, Burns GAPC, O’Neill MA, Scannell JW, Young MP (2000) Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. Philos Trans R Soc Lond Biol 355: 91–110
Hilgetag CC, Kötter R, Stephan KE, Sporns O (2002) Computational methods for the analysis of brain connectivity. In: Computational neuroanatomy. Humana Press, Totowa, NJ, pp 295–335
Holme P, Kim BJ, Yoon CN, Han SK (2002) Attack vulnerability of complex networks. Phys Rev E 65: 056109
Ito T, Chiba T, Ozawa R, Yoshida M, Hattori M, Sakaki Y (2001) A comprehensive two-hybrid analysis to explore the yeast protein interactome. Proc Natl Acad Sci USA 98: 4569–4574
Jeong H, Mason SP, Barabási A-L, Oltvai ZN (2001) Lethality and centrality in protein networks. Nature 411: 41–42
Kaiser M, Hilgetag CC (2004) Spatial growth of real-world networks. Phys Rev E 69: 036103
Keinan A, Sandbank B, Hilgetag CC, Meilijson I, Ruppin E (2004) Fair attribution of functional contribution in artificial and biological networks. Neural Comput (in press)
Kitano H (2003) Computational systems biology. Nature 420: 206–210
Martin R, Kaiser M, Andras P, Young MP (2001) Is the brain a scale-free network? Society of Neuroscience Paper 816.14
Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabási A-L (2002) Hierarchical organization of modularity in metabolic networks. Science 297: 1551–1555
Scannell JW, Blakemore C, Young MP (1995) Analysis of connectivity in the cat cerebral cortex. J Neurosci 15: 1463–1483
Scannell JW, Burns GA, Hilgetag CC, O’Neil MA, Young MP (1999) The connectional organization of the cortico-thalamic system of the cat. Cereb Cortex 9: 277–299
Schuster S, Hilgetag C (1994) On elementary flux modes in biochemical reaction systems at steady state. J Biol Syst 2: 165–182
Schwikowski B, Uetz P, Fields S (2000) A network of protein-protein interactions in yeast. Nat Biotechnol 18: 1257–1261
Sporns O (2002) Graph theory methods for the analysis of neural connectivity patterns. In: Neuroscience databases. Kluwer, Dordrecht, pp 169–183
Sporns O, Tononi G, Edelman GM (2000) Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb Cortex 10: 127–141
Stelling J, Klamt S, Bettenbrock K, Schuster S, Gilles ED (2002) Metabolic network structure determines key aspects of functionality and regulation. Nature 420: 190–193
Strogatz SH (2001) Exploring complex networks. Nature 410: 268–276
Wagner A (2000) Robustness against mutations in genetic networks of yeast. Nat Genet 24: 355–361
Watts DJ (1999) Small worlds. Princeton University Press, Princeton, NJ
Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393: 440–442
You SW, Chen B, Liu H, Lang B, Xia J, Jiao X, Ju G (2003) Spontaneous recovery of locomotion induced by remaining fibers after spinal cord transection in adult rats. Restor Neurol Neurosci 21: 39–45
Young MP (1992) Objective analysis of the topological organization of the primate cortical visual system. Nature 358: 152–155
Young MP (1993) The organization of neural systems in the primate cerebral cortex. Philos Trans R Soc 252: 13–18
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kaiser, M., Hilgetag, C. Edge vulnerability in neural and metabolic networks. Biol. Cybern. 90, 311–317 (2004). https://doi.org/10.1007/s00422-004-0479-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00422-004-0479-1