David Ethan Kennerly

## About the ArticlesThe first article, "Games within Games," introduces graph theory and demonstrates how mechanics in any game can be modeled by a mathematical graph (A mathematical graph is basically a well-defined network). Then graphs are modeled for common activities in massively multiplayer games: hunting, gathering, missions, and spatial navigation. Several case studies are analyzed, in which graph theory is used to expose exploits and suggest improvements in Anarchy Online, Ultima Online, City of Heroes, and others.The second article, "Worlds within Worlds," extends graph theory to model the economy and community in a massively multiplayer game. The economy is modeled by graphs of transactions, and the community is modeled by graphs of chatting, team participation, friendship, guild membership, and faction relationships. Examples of economic and community design are given from several online games, such as Dark Ages, Final Fantasy XI, EverQuest, and World of Warcraft.
## Making the ConnectionHere is an online appendix to a pair of articles that introduces the mathematical concepts of graph theory for use by massively multiplayer (MMP) game designers. Since this article deals with connections, it is appropriate that an online presence connect it to sites for further exploration. You will find a glossary of terms defined in the article and links for algorithms and further study.Ethan enjoys direct feedback and discussing the topic further.
## ModelMassively multiplayer (MMP) games are complex. The following figure models one suggested approach for learning about the fundamental mechanisms and systems in MMPs. The figure may be loosely interpretted as a system of prerequisites, like classes in a college degree. Each vertex (labeled point) may be considered as a type of graph. Each arc (directional line) depicts the prerequisite knowledge for subsequent graphs.
hunt graph. An arc between two vertices represents that the concept of the target depends on comprehending the concepts of the source. For example, to understand a mission graph, the reader must first comprehend the hunt graph and the gather graph.
The above figure loosely categorizes the massively multiplayer systems as:
## ArticlesFor explanation and examples of the use of these concepts, read the articles "Games within Games" and "Worlds within Worlds" inMassively Multiplayer Game Development 2 (ISBN 1-58450-390-4) published by Charles River Media, 2005.
## GlossaryThe pair of articles introduce several new terms, which a reader may find convenient to refer to in a single glossary.
## LinksThe following are useful links for game designers who wish to apply graph theory.## IntroductionIntroduction and reference on graph theory.Brent Gulanowski, "What are Videogames?" Wikipedia: Graph theory Reinhard Diestel, Graph Theory textbook ## ApplicationsA few uses of graph theory.Journal of Graph Theory Power Structure ## AlgorithmsAlgorithms to solve some graph problems.The Stony Brook Algorithm Repository Journal of Graph Algorithms and Applications ## SoftwareSoftware and implementation of graphs.Combinatorica PIGALE Graph Template Library Oracle Tip: Solving directed graph problems with SQL, part 1 ## PortalsOther sites with links on graph theory.Mongoose Metrics, Graph Theory Resource Page (links to lessons and interactive examples) http://www.mongoosemetrics.com/phone-articles/graph-theory-resource-page.php Google Directory Graph Theory: Textbooks and Resources The Mathematical Atlas: Graph Theory |
## Resources## About the author |

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