Understanding how ecological networks are assembled is important because network structure reflects ecosystem functioning and stability. Quantitative network analysis incorporates measures of interaction strength as an estimate of the magnitude of the effect of interaction partners on one another. Most plant-pollinator network studies use frequency of interaction between individual pollinators and individual plants (encounter) as a surrogate of interaction strength. However, the number of flowers visited per encounter may strongly vary among pollinator and plant species, and therefore not all encounters are quantitatively equivalent. We sampled plant-pollinator interactions in a Mediterranean scrubland and tested whether using a measure of interaction strength based on the number of flowers visited resulted in changes in species (species strength, interaction species asymmetry, specialization) and network descriptors (nestedness, H2’, interaction evenness, plant generality, pollinator generality) compared to the encounter-based measure. Several species (including some of the most abundant ones) showed important changes in species descriptors, notably in specialization. These changes were especially important in plant species with large floral displays, which became less specialized with the visit-based measure of interaction strength. At the network level we found significant changes in all properties analysed. With the encounter-based approach plant generality was much higher than pollinator generality (high specialization asymmetry between trophic levels). However, with the visit-based approach plant generality was greatly reduced so that plants and pollinators had similar levels of generalization. Interaction evenness also decreased strongly with the visit-based approach. We conclude that accounting for the number of flowers visited per encounter provides a more ecologically relevant measure of interaction strength. Our results have important implications for the stability of pollination networks and the evolution of plant-pollinator interactions. The use of a visit-based approach is especially important in studies relating interaction network structure and ecosystem function (pollination and/or exploitation of floral resources).