O. Angel, R. Van-de-hofstad, and C. Holmgren, Limit laws for self-loops and multiple edges in the configuration model, 2016.

A. Barbour and A. Röllin, Central limit theorems in the configuration model, 2017.

A. Barvinok, On the number of matrices and a random matrix with prescribed row and column sums and 0???1 entries, Advances in Mathematics, vol.224, issue.1, pp.316-339, 2010.
DOI : 10.1016/j.aim.2009.12.001

A. Barvinok and J. Hartigan, An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums. Transactions of the, pp.4323-4368, 2012.

A. Barvinok and J. Hartigan, The number of graphs and a random graph with a given degree sequence, Random Structures & Algorithms, vol.26, issue.3, pp.301-348, 2013.
DOI : 10.1016/S0895-7177(97)00210-0

F. Bergeron, G. Labelle, and P. Leroux, Combinatorial Species and Tree-like Structures, 1997.
DOI : 10.1017/CBO9781107325913

B. Bollobás, A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs, European Journal of Combinatorics, vol.1, issue.4, pp.311-316, 1980.
DOI : 10.1016/S0195-6698(80)80030-8

B. Bollobás, Threshold functions for small subgraphs, Mathematical Proceedings of the Cambridge Philosophical Society, vol.5, issue.02, pp.197-206, 1981.
DOI : 10.1007/BF02018372

B. Bollobás, J. H. Kim, and J. Verstraëte, Regular subgraphs of random graphs, Random Structures and Algorithms, vol.21, issue.1, 2006.
DOI : 10.1017/CBO9780511814068

C. Siu-on and M. Molloy, (k + 1)-cores have k-factors, Combinatorics, Probability and Computing, vol.21, issue.6, 2012.

S. Chatterjee, P. Diaconis, and A. Sly, Random graphs with a given degree sequence. The Annals of Applied Probability, pp.1400-1435, 2011.
DOI : 10.1214/10-aap728

URL : http://doi.org/10.1214/10-aap728

X. Chen, K. Nam, and T. Pospíchal, Quivers and Representations, In Handbook of Algebra. Handb. Algebr, vol.6, issue.6, pp.507-561, 2009.
DOI : 10.1016/S1570-7954(08)00209-X

G. Collet-anddanì-ele and . Gardy, Patchworks of barely balanced graphs In preparation. [14] ´ Elie de Panafieu and Lander Ramos. Graphs with degree constraints, Proceedings of the Meeting on Analytic Algorithmics and Combinatorics (Analco16), 2016.

M. Drmota, L. Ramos, and J. Rué, Subgraph statistics in subcritical graph classes. Random Structures and Algorithms, pp.631-673, 2017.
DOI : 10.1002/rsa.20721

URL : http://arxiv.org/pdf/1512.08889

P. Duchon, P. Flajolet, G. Louchard, and G. Schaeffer, Boltzmann samplers for the random generation of combinatorial structures, Combinatorics, Probability and Computing, vol.13, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00307530

P. Erd?, O. , and A. Rényi, On the evolution of random graphs. Publication of the Mathematical Institute of the Hungarian Academy of Sciences, pp.17-61, 1960.

P. Flajolet, D. E. Knuth, and B. Pittel, The first cycles in an evolving graph, Discrete Mathematics, vol.75, pp.1-3167, 1989.
URL : https://hal.archives-ouvertes.fr/inria-00075666

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009.
DOI : 10.1017/CBO9780511801655

URL : https://hal.archives-ouvertes.fr/inria-00072739

P. Gao, The First k-Regular Subgraph is Large, Combinatorics, Probability and Computing, vol.13, issue.03, pp.412-433, 2014.
DOI : 10.1016/S0195-6698(13)80042-X

P. Gao and N. Wormald, Enumeration of graphs with a heavy-tailed degree sequence, Advances in Mathematics, vol.287, pp.412-450, 2016.
DOI : 10.1016/j.aim.2015.09.002

URL : http://arxiv.org/pdf/1404.1250.pdf

Z. Gao and N. Wormald, Distribution of subgraphs of random regular graphs. Random Structures & Algorithms, pp.38-48, 2008.
DOI : 10.1002/rsa.20189

URL : http://www.math.uwaterloo.ca/~nwormald/papers/subregdist.pdf

O. Giménez and M. Noy, Asymptotic enumeration and limit laws of planar graphs, Journal of the American Mathematical Society, vol.22, issue.2, pp.309-329, 2009.
DOI : 10.1090/S0894-0347-08-00624-3

C. Greenhill, M. Isaev, and B. Mckay, Subgraph counts for dense random graphs with specified degrees, 2018.

C. Greenhill and B. Mckay, Asymptotic Enumeration of Sparse Multigraphs with Given Degrees, SIAM Journal on Discrete Mathematics, vol.27, issue.4, pp.2064-2089, 2013.
DOI : 10.1137/130913419

URL : http://arxiv.org/pdf/1303.4218.pdf

K. Walter and . Hayman, A generalisation of Stirling's formula, J. Reine Angew. Math, vol.196, pp.67-95, 1956.

S. Janson, D. E. Knuth, T. Luczak, and B. Pittel, The birth of the giant component . Random Structures and Algorithms, pp.233-358, 1993.
DOI : 10.1002/rsa.3240040303

S. Janson, T. Luczak, and A. Ruci´nskiruci´nski, Random Graphs, 2000.
DOI : 10.1002/9781118032718

S. Janson, K. Oleszkiewicz, and A. Ruci´nskiruci´nski, Upper tails for subgraph counts in random graphs, Israel Journal of Mathematics, vol.10, issue.1, pp.61-92, 2004.
DOI : 10.1007/978-3-662-04538-1

URL : http://www.math.uu.se/%7Esvante/papers/sj152.pdf

B. Jeong-han-kim, V. Sudakov, and . Vu, Small subgraphs of random regular graphs, Discrete Mathematics, vol.307, pp.1961-1967, 2007.

S. Letzter, The property of having a k-regular subgraph has a sharp threshold. Random Structures and Algorithms, pp.509-519, 2013.

B. Mckay, Subgraphs of Random Graphs with Specified Degrees, Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), 2010.
DOI : 10.1142/9789814324359_0155

B. Mckay, Subgraphs of Dense Random Graphs with Specified Degrees, Combinatorics, Probability and Computing, vol.11, issue.03, pp.413-433, 2011.
DOI : 10.1006/jcta.1996.0003

B. Mckay and N. Wormald, Asymptotic Enumeration by Degree Sequence of Graphs of High Degree, European Journal of Combinatorics, vol.11, issue.6, pp.565-580, 1990.
DOI : 10.1016/S0195-6698(13)80042-X

B. Mckay, N. Wormald, and B. Wysocka, Short cycles in random regular graphs, Electronic J. of Combinatorics, vol.11, issue.1, p.66, 2004.

D. Mitsche and M. Molloy, and Pawel Praa lat. k-regular subgraphs near the k-core threshold of a random graph, 2018.

M. Noy, C. Requilé, and J. Rué, Further results on random cubic planar graphs, 2018.

R. Pemantle and M. C. Wilson, Analytic Combinatorics in Several Variables
DOI : 10.1017/CBO9781139381864

URL : http://www.cs.auckland.ac.nz/%7Emcw/Research/mvGF/asymultseq/ACSVbook/ACSV121108submitted.pdf

P. Praa-lat, J. Verstraëte, and N. Wormald, On the threshold for k-regular subgraphs of random graphs, Combinatorica, vol.6, issue.1, pp.565-581, 2011.
DOI : 10.4153/CJM-1954-033-3

A. Ruci´nskiruci´nski, When are small subgraphs of a random graph normally distributed? Probability Theory and Related Fields, pp.1-10, 1988.

A. Ruci´nskiruci´nski and A. Vince, Strongly balanced graphs and random graphs, Journal of Graph Theory, vol.49, issue.2, pp.251-264, 1986.
DOI : 10.1017/S0305004100058655

C. Stegehuis, R. Van-der-hofstad, A. J. Janssen, and J. Van-leeuwaarden, Clustering spectrum of scale-free networks, Physical Review E, vol.96, issue.4, p.42309, 2017.
DOI : 10.1371/journal.pone.0010012

URL : https://pure.tue.nl/ws/files/79833577/PhysRevE.96.042309.pdf

R. Van-der-hofstad, Counting Graphs and Null Models of Complex Networks: Configuration Model and Extensions, Graph-Theoretic Concepts in Computer Science -43rd International Workshop, WG 2017, pp.1-17, 2017.
DOI : 10.1038/30918

R. Van-der-hofstad, Random Graphs and Complex Networks, Cambridge Series on Statistical and Probabilistic Mathematics, 2017.
DOI : 10.1017/9781316779422

R. Van-der-hofstad, A. J. Janssen, J. Van-leeuwaarden, and C. Stegehuis, Local clustering in scale-free networks with hidden variables, Physical Review E, vol.95, issue.2, pp.95-2017, 22307.
DOI : 10.1103/PhysRevLett.116.208302

R. Van-der-hofstad, J. Van-leeuwaarden, and C. Stegehuis, Optimal subgraph structures in scale-free configuration models, 2017.

R. Van-der-hofstad, J. Van-leeuwaarden, and C. Stegehuis, Triadic Closure in Configuration Models with Unbounded Degree Fluctuations, Journal of Statistical Physics, vol.65, issue.6804, 2017.
DOI : 10.1103/PhysRevE.65.066130

N. Wormald, Some problems in the enumeration of labelled graphs, Bulletin of the Australian Mathematical Society, vol.21, issue.01, 1978.
DOI : 10.1017/S0004972700011436

N. Wormald, Models of Random Regular Graphs, Surveys in Combinatorics, pp.239-298, 1999.
DOI : 10.1017/CBO9780511721335.010