Many biological materials, including the extracellular matrix, connective tissue, blood vessels and various membranes have a network of collagen/elastin fibers as their main structural constituent and are classified as Network materials. The accumulation of damage and rupture in these materials leads to pain and debilitating conditions. Therefore, it is of interest to determine the mechanisms of failure as well as the structural parameters that control damage and rupture in network materials. In this work we investigate the relation between structural parameters of the network, its architecture and its strength and toughness. We report the dependence of the strength on network density, crosslink density, degree of fiber alignment and fiber properties. We also investigate the toughness of networks without pre-existing defects as a function of the same set of structural parameters. We observe and characterize the intermittent dynamics of rupture in stochastic soft networks. The outcomes of the study are (i) structure-property relations pertaining to material rupture, and (ii) a physical picture of gradual material degradation before macroscopic fracture.