There isn't an Arduino reset button in the Mini Breakout Board. However the Edison module has two reset signals as explained on section 4.10 of the Intel® Edison Compute Module Hardware Guide. They both can be accessed through the Mini Breakout Board on pins 3 of J18 (PWRBTN) and 7 of J19 (RESET_OUT).
Thank you Peter, But if I want to make a reset button should I connect the reset_out to a pull up resistor to 1.8V and the button to the GND?
Well, not on RESET_OUT, since it is an output used to mark when the board is set to reset. But you could connect PWRBTN to a pull-up resistor to 1.8v and a button to GND. But there is a detail about PWRBTN, it's features are timed as explained on section 2.4 of the Intel® Edison Breakout Board Hardware Guide. The PWRBTN signal is connected to the power button as you can see in sheet 7 of the Intel® Edison Breakout Board Schematic.
However this is not the only way you can create a reset. You could set a GPIO as a reset through software. For example, you can set it to reboot the board if it detects a high or low signal. The same applies to a process, you can set a pin to kill certain process if it detects a high or low signal.