In graph-based extractive text summarization techniques, the weight assigned to the edges of the graph is the crucial parameter for the sentence ranking. The weights associated with the edges are based on the similarity between sentences (nodes). Most of the graph-based techniques use the common words based similarity measure to assign the weight. In this paper, we propose a new graph-based summarization technique, which, besides taking into account the similarity among the individual sentences, also considers the similarity between the sentences and the overall (input) document. While assigning the weight among the edges of the graph, we consider two attributes. The first attribute is the similarity among the nodes, which forms the edges of the graph. The second attribute is the weight given to a component that represents how much the particular edge is similar to the topics of the overall document for which we incorporate the topic modeling. Along with these modifications, we use the semantic measure to find the similarity among the nodes. The evaluation results of the proposed method demonstrate a significant improvement of the summary quality over the existing text summarization techniques.