Frugivory interactions between birds and fruit-bearing plants are shaped by the abundance of its interacting species, their temporal overlap, the matching of their morphologies, as well as fruit and seed characteristics. Our study evaluates the role of seven factors of fruits and plants in determining the frequency of whole-fruit consumption by birds. We studied the frugivory network of a Neotropical periurban park in Xalapa, Veracruz, Mexico, and quantified relative abundance and phenology of birds and fruit, as well as fruit morphology, chromatic and achromatic contrast, and nutritional content. Using a maximum likelihood approach, we compared the observed interaction network with 62 single- and multiple-variable probabilistic models. Our network is composed of 11 plants and 17 birds involved in 81 frugivory interactions. This network is nested, modular, and relatively specialized. However, the frequency of pairwise interactions is not explained by the variables examined in our probabilistic models and found the null model has the best performance. This indicates that no single predictor or combination of them is better at explaining the observed frequency of pairwise interactions than the null model. The subsequent four top-ranking models, with ΔAIC values < 100, are single-variable ones: carbohydrate content, lipid content, chromatic contrast, and morphology. Two- and three-variable models show the poorest fit to observed data. The lack of a deterministic pattern does not support any of our predictions nor neutral- or niche-based processes shaping the observed pattern of fruit consumption in our interaction network. It may also mean that fruit consumption by birds in this periurban park is a random process. Although our study failed to find a pattern, our work exemplifies how investigations done in urban settings, poor in species and interactions, can help us understand the role of disturbance in the organization of frugivory networks and the processes governing their structure.