We consider the propagation of Transverse Electric (TE) waves in a 2D photonic crystal made of an homogeneous bulk containing high permittivity identical inclusions localized at the vertices of a honeycomb lattice [1, 2]. In this high contrast regime, we analyse the band structure of the underlying elliptic operator. We prove global results on the evolution of the band structure with respect to the contrast as well as detailed local information such as the existence of Dirac points, which are conical crossings between consecutive dispersion surfaces. Our study is illustrated by numerical simulations. Moreover, essential differences between this electromagnetic setting and the quantum model of graphene [3] will be discussed during the talk.