We introduce a novel methodology for differential network analysis in two-sample problems, specifically designed for count data using Poisson regression models. The objective is to identify differences between networks under distinct conditions. We conduct node-level screening to assess whether node-conditional distributions differ across conditions. These distributions are modeled using Poisson generalized linear models, and equality is tested via likelihood ratio tests, ensuring false discovery rate control across nodes. Through a simulation study, we show that our approach has a strong performance in accurately identifying differences while maintaining false discovery rate control. Finally, we apply the method to analyze variations in the basketball statistics of the two NBA finalist teams from the 2009–2010 season: the Los Angeles Lakers and the Boston Celtics.