Classification of weighted networks through mesoscale homological features

Journal of Complex Networks

Volumn 5, Issue 2, 2017, Pages 245-273

  Sizemore, Ann ^a   Giusti, Chad ^b   Bassett, Danielle S ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Applied topology; Network classification; Persistent homology

Indexed keywords

DYNAMICAL SYSTEMS; GRAPH THEORY; TOPOLOGY;

DYNAMICAL SYSTEMS MODEL; GRAPH-THEORETIC; MESOSCALE STRUCTURE; NETWORK CLASSIFICATION; NETWORK STRUCTURES; PERSISTENT HOMOLOGY; WEIGHTED NETWORK MODELS; WEIGHTED NETWORKS;

COMPLEX NETWORKS;

EID: 85018981616     PISSN: 20511310     EISSN: 20511329     Source Type: Journal    
DOI: 10.1093/comnet/cnw013     Document Type: Article

References (64)

1. Watts, D. J. & Strogatz, S. H. (1998) Collective dynamics of 'small-world' networks. Nature, 393, 440-442.
2. Amaral, L. A. N., Scala, A., Barthelemy, M. & Stanley, H. E. (2000) Classes of small-world networks. Proc. Natl. Acad. Sci. U.S.A., 97, 11149-11152.
3. Guimera, R., Sales-Pardo, M. & Amaral, L. A. (2007) Classes of complex networks defined by role-to-role connectivity profiles. Nat. Phys., 3, 63-69.
4. Kantarci, B. & Labatut, V. (2013) Classification of complex networks based on topological properties.
5. Third International Conference on Cloud and Green Computing (CGC). Conference Proceedings, S.C. Satapathy, B.N. Biswal, S.K. Udgata, & J.K. Mandal, eds, Piscataway, NJ, USA, IEEE, 297-304.
6. Onnela, J.-P., Fenn, D. J., Reid, S., Porter, M. A., Mucha, P. J., Fricker, M. D. & Jones, N. S. (2012) Taxonomies of networks from community structure. Phys. Rev. E, 86, 036104.
7. de Solla Price, D. J. (1965) Networks of scientific papers. Science, 149, 510-515.
8. Gallai, T. (1967) Transitiv orientierbare graphen. Acta Math. Hungar., 18, 25-66.
9. Albert, R. & Barabási, A.-L. (2002) Statistical mechanics of complex networks. Rev. Mod. Phys., 74, 47.
10. Luce, R. D. & Perry,A. D. (1949) A method of matrix analysis of group structure. Psychometrika, 14, 95-116.
11. Newman, M. E. (2006) Modularity and community structure in networks. Proc. Natl. Acad. Sci. U.S.A., 103, 8577-8582.
12. Carlsson, G. (2009) Topology and data. Bull. Am. Math. Soc., 46, 255-308.
13. Ghrist, R. (2008) Barcodes: the persistent topology of data. Bull. Am. Math. Soc., 45, 61-75.
14. Ghrist, R. (2014) Elementary Applied Topology. North Charleston, South Carolina, CreateSpace Independent Publishing Platform.
15. Giusti, C., Pastalkova, E., Curto, C.Itskov,V. (2015) Clique topology reveals intrinsic geometric structure in neural correlations. Proc. Nat. Acad. Sci. USA., 112, 13455-13460.
16. Zomorodian, A. & Carlsson, G. (2005) Computing persistent homology. DCG, 33, 249-274.
17. Sizemore, A. E. (2015) Network Generation and Analysis Toolbox. https://sites.google.com/a/seas.upenn.edu/ weighted-network-toolbox/. Accessed 25 April 2016.
18. Klimm, F., Bassett, D. S., Carlson, J. M. & Mucha, P. J. (2014) Resolving structural variability in network models and the brain. PLOS Comput. Biol., 10, e1003491.
19. Lohse, C., Bassett, D. S., Lim, K. O. & Carlson, J. M. (2014) Resolving anatomical and functional structure in human brain organization: identifying mesoscale organization in weighted network representations. PLoS Comput. Biol., 10, e1003712.
20. Kahle, M. (2014) Topology of random simplicial complexes: a survey. AMS Contemp. Math., 620, 201-222.
21. Serrano, M. á. & Boguñá, M. (2005) Weighted configuration model. AIP Conf. Proc., 776, 101.
22. Li, C. & Chen, G. (2004) A comprehensive weighted evolving network model. Physica A, 343, 288-294.
23. Rubinov, M. & Sporns, O. (2010) Complex network measures of brain connectivity: uses and interpretations. Neuroimage, 52, 1059-1069.
24. Garlaschelli, D. (2009) The weighted random graph model. New J. Phys., 11, 073005.
25. Muldoon, S. F., Bridgeford, E.W. & Bassett, D. S. (2015) Small-world propensity in weighted, real-world networks. Preprint arXiv:1505.02194.
26. Barthelemy, M. (2011) Spatial networks. Phys. Rep., 499, 1-101.
27. Nickel, C. L. M. (2006) Random Dot Product Graphs: A Model for Social Networks, PhD dissertation, Baltimore, Maryland, USA, Johns Hopkins University.
28. Kahle, M. (2011) Random geometric complexes. DCG, 45, 553-573.
29. Kdahlquist, Pico, A., van Iersel, M., Kelder, T., Digles, D., Nijveen, H., Fidelman, N., Andrews II, R. & Houten, S. (2013) TCA Cycle (Homo sapiens). http://wikipathways.org/index.php?title=Pathway:WP78. Accessed 2 July 2015.
30. Szklarczyk, D., Franceschini, A., Wyder, S., Forslund, K., Heller, D., Huerta-Cepas, J., Simonovic, M., Roth, A., Santos, A., Tsafou, K. P. et al. (2014) STRING v10: protein-protein interaction networks, integrated over the tree of life. Nucleic Acids Res. 43, D447-D452.
31. Gu, S., Pasqualetti, F., Cieslak, M., Telesford, Q. K., Alfred, B. Y., Kahn, A. E., Medaglia, J. D., Vettel, J. M., Miller, M. B., Grafton, S. T. et al. (2015) Controllability of structural brain networks. Nat. Commun., 6.
32. Cammoun, L., Gigandet, X., Meskaldji, D., Thiran, J. P., Sporns, O., Do, K. Q., Maeder, P., Meuli, R. & Hagmann, P. (2012) Mapping the human connectome at multiple scales with diffusion spectrum MRI. J. Neurosci. Methods, 203, 386-397.
33. Cieslak, M. & Grafton, S. (2014) Local termination pattern analysis: A tool for comparing white matter morphology. Brain Imaging Behav., 8, 292-299.
34. Breakspear, M., Heitmann, S. & Daffertshofer, A. (2010) Generative models of cortical oscillations: neurobiological implications of the kuramoto model. Front. Hum. Neurosci., 4, 190.
35. Cumin, D. & Unsworth, C. (2007) Generalising the Kuramoto model for the study of neuronal synchronisation in the brain. Physica D, 226, 181-196.
36. Bassett, D. S.,Wymbs, N. F., Porter, M. A., Mucha, P. J. & Grafton, S. T. (2014) Cross-linked structure of network evolution. Chaos, 24, 013112.
37. Henselman, G. & Ghrist, R. A novel algorithm for topological persistence, with Application to Neuroscience.
38. Adcock, A., Carlsson, E. & Carlsson, G. (2012) The ring of algebraic functions on persistence bar codes. Preprint https://arxiv.org/abs/1304.0530. Accessed 18 December 2015.
39. Mood,A., Graybill, F.Boes, D. (1974) Introduction to the Theory of Statistics. New York, (USA), McGraw- Hill.
40. Maimon, O. & Rokach, L. (2005) Data Mining and Knowledge Discovery Handbook, vol. 2. New York City, NY, USA, Springer.
41. Kaufman, L. & Rousseeuw, P. J. (1990) Finding Groups in Data: An Introduction to Cluster Analysis. New York City, NY, USA, Wiley-Interscience.
42. Cohen-Steiner, D., Edelsbrunner,H.Harer, J. (2007) Stability of persistence diagrams.DCG, 37, 103-120.
43. Bassett, D. S., Brown, J. A., Deshpande,V., Carlson, J. M. & Grafton, S. T. (2011) Conserved and variable architecture of human white matter connectivity. Neuroimage, 54, 1262-1279.
44. Bassett, D. S., Greenfield, D. L., Meyer-Lindenberg, A.,Weinberger, D. R., Moore, S.W. & Bullmore, E. T. (2010) Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS. Comput. Biol., 6, e1000748.
45. Chen, Z. J., He, Y., Rosa-Neto, P., Germann, J. & Evans, A. C. (2008) Revealing modular architecture of human brain structural networks by using cortical thickness from MRI. Cereb. Cortex, 18, 2374-2381.
46. Braun, U., Schäfer, A.,Walter, H., Erk, S., Romanczuk-Seiferth, N., Haddad, L., Schweiger, J. I., Grimm, O., Heinz, A., Tost, H. et al. (2015) Dynamic reconfiguration of frontal brain networks during executive cognition in humans. Proc. Natl. Acad. Sci. U.S.A., 112, 11678-11683.
47. Goni, J., van den Heuvel, M. P., Avena-Koenigsberger, A., Velez de Mendizabal, N., Betzel, R. F., Griffa, A., Hagmann, P., Corominas-Murtra, B., Thiran, J. P. & Sporns, O. (2014) Resting-brain functional connectivity predicted by analytic measures of network communication. Proc. Natl. Acad. Sci. U.S.A., 111, 833-838.
48. Hermundstad, A. M., Bassett, D. S., Brown, K. S., Aminoff, E. M., Clewett, D., Freeman, S., Frithsen, A., Johnson, A., Tipper, C. M., Miller,M. B., Grafton, S. T. & Carlson, J. M. (2013) Structural foundations of resting-state and task-based functional connectivity in the human brain. Proc. Natl. Acad. Sci. U.S.A., 110, 6169-6174.
49. Hermundstad, A. M., Brown, K. S., Bassett, D. S., Aminoff, E. M., Frithsen, A., Johnson, A., Tipper, C. M., Miller, M. B., Grafton, S. T. & Carlson, J. M. (2014) Structurally-constrained relationships between cognitive states in the human brain. PLoS Comput. Biol., 10, e1003591.
50. Honey, C. J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J. P., Meuli, R. Hagmann, P. (2009) Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl. Acad. Sci. U.S.A., 106, 2035-2040.
51. Bullmore, E. & Sporns, O. (2012) The economy of brain network organization. Nat. Rev. Neurosci., 13, 336-349.
52. Niven, J. E. & Laughlin, S. B. (2008) Energy limitation as a selective pressure on the evolution of sensory systems. J. Exp. Biol., 211, 1792-1804.
53. Zhang, X., Jantama, K., Moore, J. C., Jarboe, L. R., Shanmugam, K. T. & Ingram, L. O. (2009) Metabolic evolution of energy-conserving pathways for succinate production in Escherichia coli. Proc. Natl. Acad. Sci. U.S.A., 106, 20180-20185.
54. Stolz, B. (2014) Computational Topology in Neuroscience. Master's thesis, Oxford, England, United Kingdom, University of Oxford.
55. Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C. J., Wedeen, V. J. & Sporns, O. (2008) Mapping the structural core of human cerebral cortex. PLoS Biol., 6, e159.
56. van den Heuvel, M. P. & Sporns, O. (2011) Rich-club organization of the human connectome. J. Neurosci., 31, 15775-15786.
57. Bobrowski, O. & Kahle, M. (2014) Topology of random geometric complexes: a survey. Preprint arXiv:1409.4734.
58. Sepulcre, J., Sabuncu, M. R.,Yeo, T. B., Liu, H. & Johnson, K. A. (2012) Stepwise connectivity of the modal cortex reveals the multimodal organization of the human brain. J. Neurosci., 32, 10649-10661.
59. Tomita, E., Tanaka, A. & Takahashi, H. (2006) The worst-case time complexity for generating all maximal cliques and computational experiments. Theor. Comput. Sci., 363, 28-42.
60. Cazals, F. & Karande, C. (2008) A note on the problem of reporting maximal cliques. Theor. Comput. Sci., 407, 564-568.
61. Makino, K. & Uno, T. (2004) New algorithms for enumerating all maximal cliques. Algorithm Theory-SWAT
62. Conference Proceedings, T. Hagerup, J. Katajainen, eds, New York City, NY, USA, Springer, 260-272.
63. Schmidt, M. C., Samatova, N. F., Thomas, K.Park, B.-H. (2009)Ascalable, parallel algorithm for maximal clique enumeration. J. Parallel Distrib. Comput., 69, 417-428.
64. Rubinov, M. & Sporns, O. (2011) Weight-conserving characterization of complex functional brain networks. Neuroimage, 56, 2068-2079.