Macroscale models of physically networked fluids suffer from the inability to connect directly to mesoscale processes due to nonlinearity and thus the need for closure approximations. In this paper physically networked complex fluids are modeled stochastically at the mesoscale, thus avoiding the need for closure assumptions. In the modeling and simulations the network consists of linear chains of Hookean bead-spring dumbbells. The linear chains break and reform stochastically subject to prescribed local attractive potentials. In the simulations the topology of the network is tracked allowing for quantification of the distribution of chain lengths and of individual dumbbell stretch. This formulation allows for breakage and recombination associated with local stress. Model predictions of the distributions of chain lengths and of dumbbell stretch both in equilibrium and in steady shearing are presented. As well, shear thickening and shear thinning regimes in steady shearing and relaxation after step strain are examined.