of the DissertationTelechelic associating polymer networks consist of polymer chains terminated by endgroups that have a different chemical composition than the polymer backbone. When dissolved in a solution, the endgroups cluster together to form aggregates. Their lifetime depends on temperature. At the micelle transition the temperature is sufficiently low for these aggregates to be substantial in size. At low temperature, a strongly connected reversible network is formed and the system behaves like a gel.Telechelic networks are of interest since they are representative of biopolymer networks and are widely used in medical applications and consumer products. The material properties of these polymer networks pose complex and current problems in polymer physics. Many of the most basic questions concerning these networks, such as how they deform under stress, remain unanswered. Experiments under constant shear reveal a rich variety of non-Newtonian responses, including shear thinning and shear thickening. Within the shear thinning regime, shear banding is observed: when a constant shear is applied, the system forms two coexisting bands with different shear rates. The goal of this work is to study such systems using computer simulations. A hybrid molecular dynamics/Monte Carlo simulation is used for this purpose.First we investigate how the network topology of an ensemble of telechelic polymers changes with temperature using graph theory. The aggregates are considered as nodes and the polymer chains as links between them. Our analysis shows that the degree distribution of the system is bimodal and consists of two Poissonian distributions with different average degrees. The number of nodes in each of them as well as the distribution of links depend on temperature. By comparing the eigenvalue spectra of the simulated gel networks with those of reconstructed networks, the most likely topology at each temperature is determined. Below the micelle transition the topology can be described by a robust bimodal network in which superpeer nodes are linked among themselves and all peer nodes are linked only to superpeers.At even lower temperatures the peers completely disappear leaving a structure of interconnected superpeers.Many real life networks exhibit a spatial dependence, i.e. the probability to form a link between two nodes in the network depends on the distance between them. The study of the eigenvalue spectra of the simulated gel revealed that spatial dependent networks show universal spectral properties. This led to an in-depth study of such spectra. When increasing spatial dependence in Erdös-Rényi, scale-free and smallworld networks, it is found that the spectrum changes. Due to the spatial dependence, the degree of clustering and the number of triangles increase. This results in a higher asymmetry (skewness). Our results show that the spectrum can be used to detect and quantify clustering and spatial dependence in a network.Next, we study the rheological response of the polymer network under constant sh...