Twitter is a popular microblogging service that has become a great medium for exploring emerging events and breaking news. Unfortunately, the explosive rate of information entering Twitter makes the users experience information overload. Since a great deal of tweets revolve around news events, summarising the storyline of these events can be advantageous to users, allowing them to conveniently access relevant and key information scattered over numerous tweets and, consequently, draw concise conclusions. A storyline shows the evolution of a story through time and sketches the correlations among its significant events. In this article, we propose a novel framework for generating a storyline of news events from a social point of view. Utilising powerful concepts from graph theory, we identify the significant events, summarise them and generate a coherent storyline of their evolution with reasonable computational cost for large datasets. Our approach models a storyline as a directed tree of socially salient events evolving over time in which nodes represent main events and edges capture the semantic relations between related events. We evaluate our proposed method against human-generated storylines, as well as the previous state-of-the-art storyline generation algorithm, on two large-scale datasets, one consisting of English tweets and the other one consisting of Persian tweets. We find that the results of our method are superior to the previous best algorithm and can be comparable with human-generated storylines.