yoshinoGRAPH cannot directrly export a graph in the EPS format that is a standard graphics format in LaTeX. Instead you can print a graph to an EPS file once you install a PostScript (PS) printer to your PC. I am using, for example, "Canon iR C6870 PS3" for this purpose. Even if you do not possess any PS printers, you can install them as local printers and select "FILE" as a port.
You can associate ".ygp" and ".ygz" files to yoshinoGRAPH manually. Go to the menu [Help]-[Preferences] and select the "system" tab. Press the "OK" button after ticking the corresponding items. You will be able to open a yoshinoGRAPH project file directly by double-clicking it.