Starting in Maya 2013, they have a 'DG Profiler', that was supported up until around Maya 2016, when they introduced the evaluation graph: When that happened, a whole new profiler was introduced. Because of that, I"ve kept my legacy notes in the Legacy DG Profiler tiddler. What you find here applies to Maya 2016 and newer.

Windows -> General Editors -> Profiler

The EM Shelf

If you install bonus tools, it comes with an /bonusGame/scripts/shelf_EM.mel you can load that has a bunch of beneficial tools in it.
Note, for any of them to work, you need to add another button to that shelf with this mel code:

source em_commands.mel;

You need to run that once per Maya session to get the shelf commands to work.

Finding Cycles in the Profiler

Once you have the Profiler up and a profiled frame selected, you can search for cycles in two ways:
In Maya 2016, search for the word "opaque" : Whatever it highlights are 'cycle clusters'.
In Maya 2016.5 and newer, search for "evaluateNodesInCluster".

Graphing Cycles

Cycles in the EG are bad news. The EM shelf gives you a way to graph them: If you select the node with the cycle and press the "CLUS" button, it'll create a PDF showing you the node's cycle dependencies.
This presumes you have this installed:

http://www.graphviz.org/

And this added to your system level PATH:

C:\Program Files (x86)\Graphviz2.38\bin

Problems getting OpenCL to run in Maya 2016.5 :

I had to set this env var to get OpenCL to work in Maya 2016.5:

MAYA_OPENCL_IGNORE_DRIVER_VERSION = 1

If OpenCL doesn't work, then neither with GPU Override.