Part 1: Basic Theory of Complex Networks
1. Introduction to Graphs
2. Models of networks: Random Models, Small World Models, and Recent Models on Power Law Networks
3. Properties of Complex Networks
Part 2: Structure and Dynamics of Complex Networks
1. Communities Detection and their Evolution
2. Complex system monitoring and measurements
3. Models and Methods for Dynamic Network Analysis
4. Phase Transitions on Complex Networks
Part 3: Complex Networks Optimization Techniques
1. Optimization and Approximation Algorithms on Power Law Networks
2. Hardness and Inapproxamability Results
3. Complexity of Several Problems in Complex Networks
4. New Approximation Techniques for Optimal Substructure Problems
5. Re-visit Several Classic Optimization Problems on Complex Networks
6. Mathematical Tools in Data Analysis
Part 4: Optimization in Complex Biological Systems
1. Cells, gene and molecule systems
2. Neuronal networks
3. Epidemiology in complex systems
4. Ecology systems
5. Modeling evolution
Complex Social Networks is a newly emerging (hot) topic with applications in a variety of domains, such as communication networks, engineering networks, social networks, and biological networks. In the last decade, there has been an explosive growth of research on complex real-world networks, a theme that is becoming pervasive in many disciplines, ranging from mathematics and computer science to the social and biological sciences.
Optimization of complex communication networks requires a deep understanding of the interplay between the dynamics of the physical network and the information dynamics within the network.
Although there are a few books addressing social networks or complex networks, none of them has specially focused on the optimization perspective of studying these networks. This book provides the basic theory of complex networks with several new mathematical approaches and optimization techniques to design and analyze dynamic complex networks.
A wide range of applications and optimization problems derived from research areas such as cellular and molecular chemistry, operations research, brain physiology, epidemiology, and ecology.
Can serve as a source of examples and case studies for a course in network optimization
This is the first publication of results and articles that study complex network systems from an optimization perspective
Provides an overview of the basic theory of complex networks with several new mathematical approaches and optimization techniques to design and analyze the dynamic of complex networks