"Set Theory and Graphs" in computer science

"Set Theory and Graphs" Please respond to the following:

• Reflect upon your current work and describe a problem you have solved using graphs.
• Provide an illustration of your graph by using the image tool () within your post.  
• What elements did you have to include in your graph?  How did a graph help you solve this problem?  

For example  

Most commonly, in my job, I utilize a network graph to find where devices are plugged into my network. Often, a device will lose connectivity on the network and we’ll have to find the specific interface on a specific device to investigate the issue. Routers and switches both hold a table called a MAC address table. Every networked device has a MAC address, which is a unique identifier. Routers also have a table that resolves an IP address to a specific MAC address, called an ARP table. To find where a device is located, I first look at the ARP table on a router to locate the MAC address. Next, on the same router, I look for that MAC in the MAC address table. The table will tell me which interface the MAC was learned on (in our lesson, this would be the edge).  I can then follow that interface to the distro switch and repeat the process down the line until I locate the device.

In the graph, the routers and switches are the vertices, while the cabling between them are the edges. The graph assists by giving us a visual representation of how our devices are networked together. The graph is also helpful in locating where possible transport loops could be located. 

DISCRETE MATH CLASS PLEASE NO PARAPHASING.