The construction of new power systems presents higher requirements for the Power Internet of Things (PIoT) technology. The “source-grid-load-storage” architecture of a new power system requires PIoT to have a stronger multi- source heterogeneous data fusion ability. Native graph databases have great advantages in dealing with multi-source heterogeneous data, which make them suitable for an increasing number of analytical computing tasks. However, only few existing graph database products have native support for matrix operation-related interfaces or functions, resulting in low efficiency when handling matrix calculations that are commonly encountered in power grids. In this paper, the matrix computation process is expressed by a strategy called graph description, which relies on the natural connection between the matrix and structure of the graph. Based on that, we implement matrix operations on graph database, including matrix multiplication, matrix decomposition, etc. Specifically, only the nodes relevant to the computation and their neighbors are concerned in the process, which prunes the influence of zero elements in the matrix and avoids useless iterations compared to the conventional matrix computation. Based on the graph description, a series of power grid computations can be implemented on graph database, which reduces redundant data import and export operations while leveraging the parallel computing capability of graph database. It promotes the efficiency of PIoT when handling multi-source heterogeneous data. An comprehensive experimental study over two different scale power system datasets compares the proposed method with Python and MATLAB baselines. The results reveal the superior performance of our proposed method in both power flow and N-1 contingency computations.