In the 1870s the Military built a Telegraph system that connection San Diego, Yuma, Prescott, Phoenix, Tucson, Camp Grant and proceeded easy into New Mexico to La Mesilla.
The system carried both military and civilian messages and the initial rates were $1.50 for a 10 word message from Tucson to San Diego with a $.75 charge for 5 additional words.
The Military Telegraph was phased out as private networks (that often followed the railroads) were built.
Source: PDF from The University of Arizona