These functions return values or vectors relating to how connected a network is and the number of nodes or edges to remove that would increase fragmentation.
net_density() measures the ratio of ties to the number of possible ties.
net_components() measures the number of (strong) components in the network.
net_cohesion() measures the minimum number of nodes to remove from the network needed to increase the number of components.
net_adhesion() measures the minimum number of ties to remove from the network needed to increase the number of components.
net_diameter() measures the maximum path length in the network.
net_length() measures the average path length in the network.
net_independence() measures the independence number, or size of the largest independent set in the network.
White, Douglas R and Frank Harary. 2001. "The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density." Sociological Methodology 31(1): 305-59. tools:::Rd_expr_doi("10.1111/0081-1750.00098")