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Structural relation patterns have been introduced recently to extend the search for complex patterns often hidden behind large sequences of data. This has motivated a novel approach to sequential patterns post-processing and a corresponding data mining method was proposed for Concurrent Sequential Patterns ConSP. This article refines the approach in the context of ConSP modelling, where a companion graph-based model is devised as an extension of previous work. Two new modelling methods are presented here together with a construction algorithm, to complete the transformation of concurrent sequential patterns to a ConSP-Graph representation. Customer orders data is used to demonstrate the effectiveness of ConSP mining while synthetic sample data highlights the strength of the modelling technique, illuminating the theories developed.