We deal with the problem of document representation for the task of measuring semantic relatedness between documents. A document is represented as a compact concept graph where nodes represent concepts extracted from the document through references to entities in a knowledge base such as DBpedia. Edges represent the semantic and structural relationships among the concepts. Several methods are presented to measure the strength of those relationships. Concepts are weighted through the concept graph using closeness centrality measure which reflects their relevance to the aspects of the document. A novel similarity measure between two concept graphs is presented. The similarity measure first represents concepts as continuous vectors by means of neural networks. Second, the continuous vectors are used to accumulate pairwise similarity between pairs of concepts while considering their assigned weights. We evaluate our method on a standard benchmark for document similarity. Our method outperforms state-of-the-art methods including ESA (Explicit Semantic Annotation) while our concept graphs are much smaller than the concept vectors generated by ESA. Moreover, we show that by combining our concept graph with ESA, we obtain an even further improvement.