Book excerpt: This lecture discusses the use of graph models to represent reconfigurable antennas. The rise of antennas that adapt to their environment and change their operation based on the user's request hasn't been met with clear design guidelines. There is a need to propose some rules for the optimization of any reconfigurable antenna design and performance. Since reconfigurable antennas are seen as a collection of self-organizing parts, graph models can be introduced to relate each possible topology to a corresponding electromagnetic performance in terms of achieving a characteristic frequency of operation, impedance, and polarization. These models help designers understand reconfigurable antenna structures and enhance their functionality since they transform antennas from bulky devices into mathematical and software accessible models. The use of graphs facilitates the software control and cognition ability of reconfigurable antennas while optimizing their performance. This lecture also discusses the reduction of redundancy, complexity and reliability of reconfigurable antennas and reconfigurable antenna arrays. The full analysis of these parameters allows a better reconfigurable antenna implementation in wireless and space communications platforms. The use of graph models to reduce the complexity while preserving the reliability of reconfigurable antennas allow a better incorporation in applications such as cognitive radio, MIMO, satellite communications, and personal communication systems. A swifter response time is achieved with less cost and losses. This lecture is written for individuals who wish to venture into the field of reconfigurable antennas, with a little prior experience in this area, and learn how graph rules and theory, mainly used in the field of computer science, networking, and control systems can be applied to electromagnetic structures. This lecture will walk the reader through a design and analysis process of reconfigurable antennas using graph models with a practical and theoretical outlook.