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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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Graph Theory

Graph theory --- Combinatorial analysis --- Théorie des graphes --- Congresses --- Congrès --- ELSEVIER-B EPUB-LIV-FT --- Graphes. (Congrès) --- Grafen (Congres) --- Graph theory - Congresses

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Combinatorial analysis --- Graph theory --- Analyse combinatoire --- Graphes, Théorie des --- Cliques (Théorie des graphes) --- Graphs, Theory of --- Theory of graphs --- Extremal problems --- Topology

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Graph theory in modern engineering; computer aided design, control, optimization, reliability analysis

Graph theory. --- Electrical engineering --- Graphic methods. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Extremal problems --- Combinatorial analysis --- Topology --- Computer-aided design --- Théorie des graphes --- Conception assistée par ordinateur --- ELSEVIER-B EPUB-LIV-FT --- Graphes, Théorie des

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This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. [Back cover]

Graph theory --- Graphes, Théorie des --- Grafos, Teoría de --- Combinatorics. --- Computer science. --- Math Applications in Computer Science. --- Graphes, Théorie des. --- Informatics --- Science --- Combinatorics --- Algebra --- Mathematical analysis --- Graphentheorie. --- Computer science—Mathematics. --- Discrete mathematics. --- Computer science --- Discrete Mathematics. --- Mathematical Applications in Computer Science. --- Mathematics. --- Computer mathematics --- Electronic data processing --- Mathematics --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Graphes, Théorie des.