Returnability in complex directed networks (digraphs)

Linear Algebra and Its Applications

Volumn 430, Issue 8-9, 2009, Pages 1886-1896

  Estrada, Ernesto ^a,b   Hatano, Naomichi ^b  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

05C20; 05C50; 05C75; 05C90; 15A18; Complex networks; Digraphs; Estrada index; Graph spectrum; Reciprocity

Indexed keywords

05C20; 05C50; 05C75; 05C90; 15A18; COMPLEX NETWORKS; DIGRAPHS; ESTRADA INDEX; GRAPH SPECTRUM; RECIPROCITY;

EID: 61449085427     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.09.033     Document Type: Article

References (40)

1. Albert R., and Barabási A.-L. Statistical mechanics of complex networks. Rev. Modern Phys. 74 1 (2002) 47-97
2. Newman M.E.J. The structure and function of complex networks. SIAM Rev. 45 (2003) 167-256
3. Newman M.E.J., Strogatz S.H., and Watts D.J. Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64 (2001) 026118
4. Dorogovtsev S.N., Mendes J.J.F., and Samukhin A.N. Giant strongly connected component of directed networks. Phys. Rev. E 64 (2001) 025101R
5. Sánchez A.D., López J.M., and Rodri{dotless}́guez M.A. Nonequilibrium phase transitions in directed small-world networks. Phys. Rev. Lett. 88 (2002) 048701
6. Jeong H., Tombor B., Albert R., Oltvai Z.N., and Barabási A.-L. The large-scale organization of metabolic networks. Nature 407 (2000) 651-654
7. Ma H., and Zeng A.-P. Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms. Bioinformatics 19 (2003) 270-277
8. Tanaka R. Scale-rich metabolic networks. Phys. Rev. Lett. 94 (2005) 168101
9. Cohen J.E., Briand F., and Newman C.M. Community Food Webs: Data and Theory (1990), Springer, Berlin
10. Pascual M., and Dunne (eds) J.A. Ecological Networks: Linking Structure to Dynamics in Food Webs (2006), Oxford University Press, Oxford
11. Stouffer D.A., Camacho J., Jiang W., and Amaral L.A.N. Evidence for the existence of a robust pattern of prey selection in food webs. Proc. Roy. Soc. B 274 (2007) 1931-1940
12. Wasserman S., and Faust K. Social Network Analysis. Methods and applications (1994), Cambridge University Press, Cambridge
13. Dutta B., and Jackson M.O. The stability and efficiency of directed communication networks. Rev. Econom. Des. 5 (2000) 251-272
14. Pastor-Satorras R., and Vespignani A. Evolution and Structure of the Internet. A Statistical Physics Approach (2004), Cambridge University Press, Cambridge
15. Gao L. On inferring autonomous system relationships in the Internet. IEEE/ACM Trans. Networking 9 (2001) 733-745
16. Garlaschelli D., and Loffredo M.I. Patterns of link reciprocity in directed networks. Phys. Rev. Lett. 93 (2004) 268701
17. Boguñá M., and Serrano M.A. Generalized percolation in random directed networks. Phys. Rev. E 72 (2005) 016106
18. Zlatić V., Božičević M., Štefančić H., and Domazet M. Wikipedias: collaborative web-based encyclopedias as complex networks. Phys. Rev. E 74 (2006) 016115
19. Serrano M.A., Maguitman A., Boguñá M., and Vespignani A. Decoding the structure of the WWW: a comparative analysis of Web crawls. ACM Trans. Web 1 (2007) 10
20. Garlaschelli D., and Loffredo M.I. Multispecies grand-canonical models for networks with reciprocity. Phys. Rev. E 73 (2006) 015101
21. Zamora-López G., Zlatić V., Zhou C., Štefančić H., and Kurths J. Reciprocity of networks with degree correlations and arbitrary degree sequences. Phys. Rev. E 77 (2008) 016106
22. Estrada E., and Rodri{dotless}́guez-Velázquez J.A. Subgraph centrality in complex networks. Phys. Rev. E 71 (2005) 056103
23. de la Peña J.A., Gutman I., and Rada J. Estimating the Estrada index. Linear Algebra Appl. 427 (2007) 70-76
24. Gutman I., and Graovac A. Estrada index of cycles and paths. Chem. Phys. Lett. 436 (2007) 294-296
25. Ginosar Y., Gutman I., Mansour T., and Schork M. Estrada index and Chebyshev polynomials. Chem. Phys. Lett. 454 (2008) 145-147
26. Carbó-Dorca R. Smooth function topological structure descriptors based on graph-spectra. J. Math. Chem. 44 (2008) 373-378
27. Estrada E., and Hatano N. Statistical-mechanical approach to subgraph centrality in complex networks. Chem. Phys. Lett. 439 (2007) 247-251
28. Estrada E., and Rodri{dotless}́guez-Velázquez J.A. Spectral measures of bipartivity in complex networks. Phys. Rev. E 72 (2005) 046105
29. Estrada E. Spectral scaling and good expansion properties in complex networks. Europhys. Lett. 73 (2006) 649-655
30. Cvetković D., Rowlinson P., and Simić S. Eigenspaces of Graphs (1997), Cambridge University Press, Cambridge
31. Bang-Jensen J., and Gutin G. Digraphs: Theory, Algorithms and Applications (2002), Springer-Verlag, Berlin
32. Janiszowski K.B. Inversion of square matrices in processors with limited calculation abilities. Int. J. Appl. Math. Comput. Sci. 13 (2003) 199-204
33. E. Estrada, D.J. Higham, Network properties revealed through matrix functions, University of Strathclyde Mathematics Research Report, 2008, #17.
34. Milo R., Shen-Orr S., Itzkovitz S., Kashtan N., Chklovskii D., and Alon U. Network motifs: Simple building blocks of complex networks. Science 298 (2002) 824-827
35. Milo R., Itzkovitz S., Kashtan N., Levitt R., Shen-Orr S., Ayzenshtat I., Sheffer M., and Alon U. Superfamilies of evolved and designed networks. Science 303 (2002) 1538-1542
36. Hummon N.P., Doreian P., and Freeman L.C. Analyzing the structure of the centrality literature between 1948 and 1979. Sci. Comm. 11 (1990) 459-480
37. de Nooy W., Mrvar A., and Batagelj V. Exploratory Social Network Analysis with Pajek (2004), Cambridge University Press, Cambridge
38. Faloutsos M., Faloutsos P., and Faloutsos C. On power-law relationships of the Internet topology. ACM SIGCOMM Comp. Comm. Rev. 29 (1999) 251-262
39. de Jesus Holanda A., Torres Pisa I., Kinouchi O., Souto Martinez A., and Seron Ruiz E.E. Thesaurus as a complex network. Physica A 344 (2004) 530-536
40. Chung F., and Lu L. Complex Graphs and Networks (2006), American Mathematical Society, Providence