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Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance. The book is self-contained, and requires only an undergraduate mathematical background.

Mathematics. --- Complex Systems. --- Graph Theory. --- Mathematical Applications in the Physical Sciences. --- Complex Networks. --- Mathématiques --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- System theory. --- Mathematical physics. --- Graph theory. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Physical mathematics --- Physics --- Systems, Theory of --- Systems science --- Science --- Math --- Extremal problems --- Mathematics --- Philosophy --- Applications of Graph Theory and Complex Networks.