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Evolutionary Graph Theory

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Book cover Diffusion in Social Networks

Part of the book series: SpringerBriefs in Computer Science ((BRIEFSCOMPUTER))

Abstract

Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this chapter, we describe the original framework for EGT and the major work that has followed it. Here, we will study the calculation of the “fixation probability”—the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results.

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Notes

  1. 1.

    There is the exception of an alternating state where every edge connects a mutant-resident pair. This state cannot be reached if it exists.

  2. 2.

    We use the shorter BD and DB notation for the update rules with birth bias BD-B and DB-B. See Table 6.2.

  3. 3.

    The authors of [26] also note that mathematically, “IM updating can be obtained from DB updating by adding loops to every vertex”.

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Authors and Affiliations

  1. School of Computing, Informatics and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA

    Paulo Shakarian

  2. Arizona State University, Tempe, AZ, USA

    Abhinav Bhatnagar, Ashkan Aleali, Elham Shaabani & Ruocheng Guo

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  1. Paulo Shakarian
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Shakarian, P., Bhatnagar, A., Aleali, A., Shaabani, E., Guo, R. (2015). Evolutionary Graph Theory. In: Diffusion in Social Networks. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-23105-1_6

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  • DOI: https://doi.org/10.1007/978-3-319-23105-1_6

  • Publisher Name: Springer, Cham

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