fMRI is a unique non-invasive approach for understanding the functional organization of the human brain, and task-based fMRI promotes identification of functionally relevant brain regions associated with a given task. Here, we use fMRI (using the Poffenberger Paradigm) data collected in mono- and dizygotic twin pairs to propose a novel approach for assessing similarity in functional networks. In particular, we compared network similarity between pairs of twins in task-relevant and task-orthogonal networks. The proposed method measures the similarity between functional networks using a geodesic distance between graph Laplacians. With method we show that networks are more similar in monozygotic twins compared to dizygotic twins. Furthermore, the similarity in monozygotic twins is higher for task-relevant, than task-orthogonal networks.