Title: Properties of interaction networks, structure coefficients, and benefit-to-cost ratios,
Abstract: In structured populations the spatial arrangement of cooperators and
defectors on the interaction graph together with the structure of the graph
itself determines the game dynamics and particularly whether or not fixation of
cooperation (or defection) is favored. For a single cooperator (and a single
defector) and a network described by a regular graph the question of fixation
can be addressed by a single parameter, the structure coefficient. As this
quantity is generic for any regular graph, we may call it the generic structure
coefficient. For two and more cooperators (or several defectors) fixation
properties can also be assigned by structure coefficients. These structure
coefficients, however, depend on the arrangement of cooperators and defectors
which we may interpret as a configuration of the game. Moreover, the
coefficients are specific for a given interaction network modeled as regular
graph, which is why we may call them specific structure coefficients. In this
paper, we study how specific structure coefficients vary over interaction
graphs and link the distributions obtained over different graphs to spectral
properties of interaction networks. We also discuss implications for the
benefit-to-cost ratios of donation games.