A well-balanced overview of mathematical approaches to complex systems ranging from applications in chemistry and ecology to basic research questions on network complexity. Matthias Dehmer, Abbe Mowshowitz, and Frank Emmert-Streib, well-known pioneers in the fi eld, have edited this volume with a view to balancing classical and modern approaches to ensure broad coverage of contemporary research problems. The book is a valuable addition to the literature and a must-have for anyone dealing with network compleaity and complexity issues.

A well-balanced overview of mathematical approaches to complex systems ranging from applications in chemistry and ecology to basic research questions on network complexity. Matthias Dehmer, Abbe Mowshowitz, and FrankEmmert-Streib, well-known pioneers in the fi eld, have edited this volume with a view to balancing classical and modern approaches to ensure broad coverage of contemporary research problems.The book is a valuable addition to the literature and a must-have for anyone dealing with network compleaity and complexity issues.

Functional Complexity Based on Topology (Hildegard Meyer-Ortmanns)Connections between Artificial Intelligence, Computational Complexity and the Complexity of Graphs (Ángel Garrido)Selection Based Estimates of Complexity Unravel Some Mechanisms and Selective Pressures Underlying the Evolution of Complexity in Artificial Networks (Hervé Le Nagard, Olivier Tenaillon)Three Types of Network Complexity Pyramid (Fang Jin-Qing, Li Yong, Liu Qiang)Computational Complexity of Graphs (Stasys Jukna)The Linear Complexity of a Graph (David L. Neel, Michael E. Orrison)Kirchhoff's Matrix Tree Theorem revisited: Counting Spanning Trees with the Quantum Relative Entropy (Vittorio Giovannetti, Simone Severini)Dimension Measure for Complex Networks (O. Shanker)Information Based Complexity of Networks (Russell K. Standish)Thermodynamic Depth in Undirected and Directed Networks (Francisco Escolano, Edwin R. Hancock)Circumscribed Complexity in Ecological Networks (Robert E. Ulanowicz)Metros as Biological Systems: Complexity in Small Real-life Networks (Sybil Derrible)