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.

Includes a tutorial overview on random graphs, with rigorous mathematical results Applies statistical physics methods to distributed algorithms Introduces the reader to graphical models and message-passing algorithms Presents the information theoretic aspects of wireless communication networks Includes supplementary material: sn.pub/extras