TITLE: Difference between connected vs strongly connected vs complete graphs
QUESTION [11 upvotes]: What is the difference between
connected
strongly-connected and
complete?
My understanding is:
connected: you can get to every vertex from every other vertex.
strongly connected: every vertex has an edge connecting it to every other vertex.
complete: same as strongly connected.
Is this correct?

REPLY [3 votes]: It is also important to remember the distinction between strongly connected and unilaterally connected. A directed graph is unilaterally connected if for any two vertices a and b, there is a directed path from a to b or from b to a but not necessarily both (although there could be). Strongly connected implies that both directed paths exist. This means that strongly connected graphs are a subset of unilaterally connected graphs.
And a directed graph is weakly connected if it's underlying graph is connected.