Relating size and functionality in human social networks through complexity
Bruce J. West, Giovanni Francesco Massari, Garland Culbreth, Roberto Failla, Mauro Bologna, Robin Dunbar, Paolo Grigolini
Abstract
Significance Dunbar hypothesized, on the basis of empirical evidence, that a typical individual can have a stable relation with at most 150 other people. We establish that this number results from the internal dynamics of a complex network. Two network models having phase transitions are used to determine the optimal size for the most efficient information exchange. Such criticality generates intermittent events, with time intervals between successive events being independent (renewal) and scaling. The scaling index depends nonmonotonically on network size and direct calculations show that the index is maximum for networks the size of the Dunbar number and provides maximal information exchange efficiency. This result provides a theory-based bridge to span the conceptual gap between psychology and sociology.