The study of the dynamic relationship between topological structure of a transit network and the mobility patterns of transit vehicles on this network is critical towardsdevising smart and time-aware solutions to transit management and recommendation systems. This paper proposes a time-varying graph (TVG) to model thisrelationship. The effectiveness of this proposed model has been explored by implementing the model in Neo4j graph database using transit feeds generated by bus transit network of the City of Moncton, New Brunswick, Canada. Dynamics in this relationshipalsohave been detected using network metrics such as temporal shortest paths, degree, betweenness and PageRank centralities as well as temporal network diameter and density. Keywords: Transit Networks,Mobility Pattern,Time-Varying Graph model, Graph Databaseand Graph Analytics Keywords: Transit Networks,Mobility Pattern,Time-Varying Graph model, Graph Database and Graph Analytics