Due to exponential growth of complex data, graph structure has become increasingly important to model various entities and their interactions, with many interesting applications including, bioinformatics, social network analysis, etc. Depending on the complexity of the data, the underlying graph model can be a simple directed/undirected and/or weighted/un-weighted graph to a complex graph (aka multi-attributed graph) where vertices and edges are labelled with multi-dimensional vectors. In this paper, we present a novel weighted distance measure based on weighted Euclidean norm which is defined as a function of both vertex and edge attributes, and it can be used for various graph analysis tasks including classification and cluster analysis. The proposed distance measure has flexibility to increase/decrease the weightage of edge labels while calculating the distance between vertex-pairs. We have also proposed a MAGDist algorithm, which reads multi-attributed graph stored in CSV files containing the list of vertex vectors and edge vectors, and calculates the distance between each vertex-pair using the proposed weighted distance measure. Finally, we have proposed a multi-attributed similarity graph generation algorithm, MAGSim, which reads the output of MAGDist algorithm and generates a similarity graph that can be analysed using classification and clustering algorithms. The significance and accuracy of the proposed distance measure and algorithms is evaluated on Iris and Twitter data sets, and it is found that the similarity graph generated by our proposed method yields better clustering results than the existing similarity graph generation methods.