Estimate of the integral photon flux in the region of extremely high energies in complex Yakutsk EAS array data

A complex analysis of Yakutsk EAS array data has been performed in order to search for primary photons generating extensive air showers with energies above 10$^{18}$ eV. Analyzing calculations and experimental data, selection criteria have been formulated and used to make a sample of showers close in their characteristics to showers initiated by primary photons. An upper limit of the integral photon flux in cosmic rays of extremely high energies has been estimated from these data.