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Directed graphs. --- Representations of graphs. --- Graph theory.

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The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Random graphs --- Graphes aléatoires --- Graphes aléatoires --- Discrete mathematics --- Random graphs. --- Graphs, Random --- Graph theory

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Covering a wide range of Random Graphs subjects, this volume examines series-parallel networks, properties of random subgraphs of the n-cube, random binary and recursive trees, random digraphs, induced subgraphs and spanning trees in random graphs as well as matchings, hamiltonian cycles and closure in such structures. Papers in this collection also illustrate various aspects of percolation theory and its applications, properties of random lattices and random walks on such graphs, random allocation schemes, pseudo-random graphs and reliability of planar networks. Several open problems

Discrete mathematics --- Combinatorial analysis --- Random graphs --- Probabilities --- Congresses --- Graphs, Random --- Graph theory --- Random graphs - Congresses --- Probabilities - Congresses --- Combinatorial analysis - Congresses

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Random graphs --- Graphes aléatoires --- Graphes aléatoires

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Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails.The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersectio

Perfect graphs. --- Graph theory --- Perfect graphs --- Graphes parfaits --- ELSEVIER-B EPUB-LIV-FT