Networks can exhibit an abrupt transition in the form of a spontaneous self-organization of a sizable fraction of the population into a giant component of connected members. This behavior has been demonstrated in random graphs under suppressive rules that passively or actively attempt to delay the formation of the giant cluster. We show that suppressive rules are not a necessary condition for a sharp transition at the percolation threshold. Rather, a finite system with aggressive tendency to form a giant cluster may exhibit an instability at the percolation threshold that is relieved through an abrupt and discontinuous transition to the stable branch. We develop the theory for a class of equilibrated networks that produce this behavior and find that the discontinuous jump is especially pronounced in small networks but disappears when the size of the system is infinite.
|Original language||English (US)|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - May 5 2015|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics