Reproducing Graphs

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Many real world networks grow because structures within get replicated. We introduce a class of models within which networks change because the vertices within them reproduce. This happens deterministically so each vertex simultaneously produces an offspring every update. These offspring could represent individuals, companies, proteins or websites. The connections given to these offspring depends upon their parents connectivity much as a child is likely to interact with their parent's friends or a new website may copy the links of pre-existing one. Adding game theory in to these simple models can lead to highly complex dynamics where small initial structures grow and break into large collections of self replicating structures