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Abstract: The paper proposes a methodology to assist the designer at the initial stages of the design synthesis process by enabling him/her to employ knowledge and algorithms existing in graph network theory. The proposed method comprises three main stages: transforming the synthesis problem into a graph theoretic problem; devising the topology possessing special engineering properties corresponding to the system requirements; finding the geometric configuration of that topology that will possess the desired properties. To clarify the idea and to demonstrate its generality, the approach is presented through three synthesis case studies from different engineering domains: electrical networks, statics and kinematics. As is highlighted in the paper, the approach of employing graph theory in the synthesis process offers several unique advantages. Among these advantages are: gaining a general perspective on different synthesis problems from different engineering domains by transforming them into the same graph problem; employing the same graph algorithms for different synthesis problems; establishing the existence of configurations with special properties solely from the topology of the system; transferring knowledge and methods between different engineering disciplines for both the topology and the geometry generation steps. [Copyright &y& Elsevier]