In this work, we investigate similarity transfer in transition metal networks from a graph-theoretical perspective. Using binary compound data, we construct large-scale chemical element networks comprising more than 2000 edges. Within this framework, we define similarity transfer ratio (ST) as a new graph-theoretical descriptor that quantifies how similarity between elements can be propagated through mediating neighbors. Three fundamental transfer mechanisms―horizontal, vertical, and diagonal―are formally characterized, and their mathematical properties, including symmetry and topological inequalities, are rigorously proven. Analysis of 29 transition metals shows that more than 79% of ST values exceed 90%, demonstrating the robustness of similarity transfer as a structural feature of chemical networks. Beyond its chemical interpretation, the ST framework complements classical graph-theoretical indices such as Wiener and Randić descriptors by capturing the transferability of similarity rather than measuring only static adjacency or distance. This study bridges network topology and chemical graph theory, establishing a transferable and quantifiable descriptor that offers new insights into periodic trends. In addition, the framework suggests potential for guiding compound prediction, although its primary contribution lies in extending the mathematical foundations of chemical similarity.