Giant Component in Random Multipartite Graphs with given Degree Sequences

References

• Bender, E. A. and Canfield, E. R. (1978). The asymptotic number of labelled graphs with given degree sequences. Journal of Combinatorial Theory 24 296–307. MR0505796Google Scholar
• Bollobás, B. (1985). Random Graphs. Academic Press.Google Scholar
• Bollobás, B., Janson, S. and Riordan, O. (2007). The phase transition in inhomogeneous random graphs. Random Structures and Algorithms 31 3–122. MR2337396Google Scholar
• Bollobás, B. and Riordan, O. (2012). An old approach to the giant component problem.Google Scholar
• Boss, M., Elsinger, H., Summer, M. and Thurner, S. (2004). Network topology of the interback market. Quantitative Finance 4.Google Scholar
• Chen, N. and Olvera-Cravioto, M. (2013). Directed random graphs with given degree distributions. Arxiv.org 1207.2475. MR3353470Google Scholar
• Erdős, P. and Rényi, A. (1960). On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutato Int. Kozl 5 17–61. MR0125031Google Scholar
• Gamarnik, D. and Misra, S. Hardness of MAX-CUT in bounded degree graphs with random edge deletions (in preparation).Google Scholar
• Goh, K., Cusick, M. E., Valle, D., Childs, B., Vidal, M. and Barabasi, A. (2007). The human disease network. PNAS 104.Google Scholar
• Jackson, M. O. (2008). Social and Economic Networks. Princeton University Press. MR2435744Google Scholar
• Janson, S. and Luczak, M. (2008). A new approach to the giant component problem. Random Structures and Algorithms 37 197–216. MR2490288Google Scholar
• Kang, M. and Seierstad, T. G. (2008). The critical phase for random graphs with a given degree sequence. Combinatorics, Probability and Computing 17 67–86. MR2376424Google Scholar
• Kesten, H. and Stigum, B. P. (1966). A limit theorem for multidimensional Galton-Watson processes. The Annals of Mathematical Statistics 37 1211–1223. MR0198552Google Scholar
• Misra, S. (2014). Decay of correlations and inference in graphical models. PhD thesis, Massachusetts Institute of Technology.Google Scholar
• Molloy, M. and Reed, B. (1995). A critical point for random graphs with a given degree sequence. Random Structures and Algorithms 6 161–180. MR1370952Google Scholar
• Molloy, M. and Reed, B. (1998). The size of the largest component of a random graph on a fixed degree sequence. Combinatorics, Probability and Computing 7 295–306. MR1664335Google Scholar
• Morrision, J. L., Breitling, R., Higham, D. J. and Gilbert, D. R. (2006). A lock-and-key model for protein-protein interactions. Bioinformatics 22.Google Scholar
• Newmann, M. E. J., Strogatz, S. H. and Watts, D. J. (2001). Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64.Google Scholar
• Riordan, O. (2012). The phase transition in the configuration model. Combinatorics, Probability and Computing 21. MR2900063Google Scholar
• van der Hofstad, R., Hooghiemstra, G. and Mieghem, P. V. (2005). Distances in random graphs with finite variance degrees. Random Structures and Algorithms 27 76–123. MR2150017Google Scholar
• van der Hofstad, R., Hooghiemstra, G. and Znamenski, D. (2005a). Random graphs with arbitrary iid degrees. Arxiv.org math/0502580.Google Scholar
• van der Hofstad, R., Hooghiemstra, G. and Znamenski, D. (2005b). Distances in random graphs with finite mean and infinite variance degrees. Eurandom.Google Scholar
• Wormald, N. C. (1978). Some problems in the enumeration of labelled graphs. PhD thesis, Newcastle University.Google Scholar
• Wormald, N. C. (1995). Differential equations for random processes and random graphs. Annals of Applied Probability 5 1217–1235. MR1384372Google Scholar
• Yildrim, M., Goh, K., Cusick, M. E., Barabasi, A. and Vidal, M. (2007). Drug-target network. Nat Biotechnol 25.Google Scholar