We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm suitable for practical use both because of its ability to generate very large graphs (efficiency) and because it is easy to implement (simplicity). We focus on a family of heuristics for which we introduce optimality conditions, and show how this optimality can be reached in practice. We then propose a different approach, specifically designed for real-world degree distributions, which outperforms the first one. Based on a conjecture which we discuss rigorously and study empirically, we finally reduce the best asymptotic complexity bound known so far.

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**Contribution à la qualité des informations dans les réseaux sociaux : Identifier et analyser les motifs récurrents pour détecter les phénomènes sociaux**Manel Mezghani*2017, March 16, Room 24-25/405*- affinity index algorithm analysis antipaedo attack bipartite blog network blogs capitalisme social Cascade centrality clustering communities community detection community structure complex network complex networks complex systems compression connected graphs data mining debian degree distribution degree peeling diameter diffusion diffusion phenomena distributed measurements DynamicNetworks dynamics edge-Markovian evolving graph eDonkey ego-centered ego-centered communities email epidemiology event detection evolving graphs evolving networks exploration failure fixed points formal concepts gossip graph graph algorithm graph decompositions Graphs hierarchical clustering honeypot influence influence ranking interaction networks internal links internet Internet topology intrinsic time IP-level ip exchanges lattice leaders link prediction long term communities markovian model measurement mesure d’influence metrics Metrology mobile networks Modelling modularity multi-ego-centered communities multi-scale multipartite graph network dynamics node proximity node similarity opinion dynamics outliers p2p P2P dynamics P2P networks parametric paris paris-traceroute path-vector routing pedophile activity phone power-law radar random graph random walks reachability robustness routing routing tables scale-free security simulation simulations sir social networks spreading spreading cascades stability statistical analysis stochastic process three-state cellular automata time-varying Topology traceroute triangles twitter UDP user profiles viral marketing visualization web wifi