Algorithms

it iwas originally introduced to measure the centrality of the nodes in networks. By definition, most of the shortest paths in a network go throught the nodes with high betweenness.

Burning Algorithms or Breadth-First Search (Solomonoff and Rapoprt,1951)

Derive an iteration relation for the weak connectivity by reasoning about the behavior of a simple component-finding alogrithms.  This result leads them to conclude that the average component size depends crucially on the mean degree a, where the degree again is the number of edges connected to a vertex. 

Percolation Theory (Stauffer and Aharony 1992; Bunde and Havlin 1994, 1996)

like the random graphs, one studes the properties of the system in which the bonds on a lattice or network are either occupied or not with some occupation probability p, asking question such as what the mean sized are of the clutster of lattice sites connected together by occupied bonds, and whether or not there exists a "spanning cluter" in the limit of large system size.