Many problems in graph theory are so hard in general that they seem hopeless. So sometimes mathematicians lower our expectations a bit, and try to prove that a statement is true for "almost all graphs" (for some reasonable interpretation of what that means) rather than insisting on proving it for all graphs. One way to address questions about about almost all graphs to use a random graph model, the first of which is due to Erdos, Rényi and Gilbert in the 1950's. Since then many more models have been introduced, but they all generate graphs according to the outcome of a random experiment. Another reason to study random graphs is for their resemblance to real-world graphs.
WMU ScholarWorks Citation
Bennett, Patrick; Cushman, Ryan; and Dudek, Andrzej, "Alternating Connectivity in Random Graphs" (2020). Faculty Research and Creative Activities Award (FRACAA). 99.