Abstract: Temporal networks are an effective way to encode temporal information into graph data losslessly. Finding the bursting cohesive subgraph (BCS), which accumulates its cohesiveness at the fastest rate, is an important problem in temporal networks. The BCS has a large number of applications, such as representing emergency events in social media, traffic congestion in road networks and epidemic outbreak in communities. Nevertheless, existing methods demand the BCS lasting for a time interval, which neglects the timeliness of the BCS. In this paper, we design an early bursting cohesive subgraph (EBCS) model based on the k-core to enable identifying the burstiness as soon as possible. To find the EBCS, we first construct a time weight graph (TWG) to measure the bursting level by integrating the topological and temporal information. Then, we propose a global search algorithm, called GS-EBCS, which can find the exact EBCS by iteratively removing nodes from the TWG. Further, we propose a local search algorithm, named LS-EBCS, to find the EBCS by first expanding from a seed node until obtaining a candidate k-core and then refining the k-core to the result subgraph in an optimal time complexity. Subsequently, considering the situation that the massive temporal networks cannot be completely put into the memory, we first design an I/O method to build the TWG and then develop I/O efficient global search and local search algorithms, namely I/O-GS and I/O-LS respectively, to find the EBCS under the semi-external model. Extensive experiments, conducted on four real temporal networks, demonstrate the efficiency and effectiveness of our proposed algorithms. For example, on the DBLP dataset, I/O-LS and LS-EBCS have comparable running time, while the maximum memory usage of I/O-LS is only 6.5 MB, which is much smaller than that of LS-EBCS taking 308.7 MB.