Family members' satisfaction with one another is central to creating healthy and supportive family environments. In this work, we propose and implement a novel computational technique aimed at exploring the possible relationship between the topology of a given family tree graph and its members' satisfaction with one another. Through an extensive empirical evaluation ($N=486$ families), we show that the proposed technique brings about highly accurate results in predicting family members' satisfaction with one another based solely on the family graph's topology. Furthermore, the results indicate that our technique favorably compares to baseline regression models which rely on established features associated with family members' satisfaction with one another in prior literature.