Dear all, we are pleased to announce the following seminar by Dr. Anna Gallo (IMT School for Advanced Studies Lucca) on *Thursday, January 15th 2026,* starting at 11:00 in room 4057, the Department of Statistics and Quantitative Methods, University of Milano-Bicocca (Milan): *Rethinking balance theory: a probabilistic approach to the study of signed networks* *Abstract:* Networks provide a powerful language to model interacting systems by representing their units as nodes and the interactions between them as links. Interactions can be connotated in several ways, such as binary/weighted, undirected/directed, etc. In the present talk we focus on the positive/negative connotation- modelling trust/distrust, alliance/enmity, friendship/conflict, etc. - by considering the so-called signed networks. Rooted in balance theory, a psychological framework that has been proposed to model human relationships, the study of signed networks has found application in fields as different as biology, ecology, economics. Here we approach it from the perspective of statistical physics, by extending the framework of Exponential Random Graph Models to the class of binary, un/directed, signed networks and employing it to assess the significance of frustrated patterns in biological, economic and social networks. The degree of balance critically depends on i) the considered system and ii) the employed benchmark: while social networks align with balance theory - with heterogeneous null models supporting its strong version and homogeneous null models supporting its weak version, biological networks often exhibit a pronounced level of frustration. For what concerns binary, directed networks, instead, we explore the relationship between frustration and reciprocity and suggest an alternative interpretation of balance in the light of directionality. Finally, we investigate signed structures at the mesoscopic scale by evaluating the tendency of a configuration to be either `traditionally' or `relaxedly' balanced. For further information, please write to *rosanna.grassi@unimib.it <rosanna.grassi@unimib.it>* Best regards.