Marketers employ various online advertising channels to reach customers, and they are particularly interested in attribution for measuring the degree to which individual touchpoints contribute to an eventual conversion. The availability of individual customer-level path-to-purchase data and the increasing number of online marketing channels and types of touchpoints bring new challenges to this fundamental problem. We aim to tackle the attribution problem with finer granularity by conducting attribution at the path level. To this end, we develop a novel graphical point process framework to study the direct conversion effects and the full relational structure among numerous types of touchpoints simultaneously. Utilizing the temporal point process of conversion and the graphical structure, we further propose graphical attribution methods to allocate proper path-level conversion credit, called the attribution score, to individual touchpoints or corresponding channels for each customer's path to purchase. Our proposed attribution methods consider the attribution score as the removal effect, and we use the rigorous probabilistic definition to derive two types of removal effects. We examine the performance of our proposed methods in extensive simulation studies and compare their performance with commonly used attribution models. We also demonstrate the performance of the proposed methods in a real-world attribution application.