Electrical Impedance Tomography (EIT) is an imaging technique with advantages of non-intrusiveness, low-cost and high temporal resolution, which is promising for multiphase flow instrumentation. However, it produces smooth images with low spatial resolution where the interface between phases cannot be distinguished and from which the phase fraction cannot be estimated correctly. In this article, an eigenvalue analysis of EIT raw data is used to estimate the void fraction, i.e. the phase area ratio in 2D, without reconstructing images. For a given EIT sensor, each acquisition frame is represented by an impedance matrix whose eigenvalues are computed after normalization. The main characteristics of the eigenvalue distribution for different two-phase flow patterns within a cylindrical pipe are analyzed numerically. The behaviors of the leading eigenvalue and of the sum of the absolute values of the following ones are assessed as functions of the void fraction. This leads to an estimation of the two-phase flow void fraction based on the characteristics of the EIT sensor configuration. The presented numerical results highlight the existing correlation between the eigenvalues and the void fraction for the phase distribution patterns considered. These simulation results are compared with experimental static tests for validation.