I want to know What it is and whether there is a difference in the definition when looking at undirected and directed graphs?
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$\begingroup$At the risk of stating the obvious...
To create a graph, you start with a set of nodes (or vertices). These are essentially points in space - a bunch of dots. Then you add a set of arcs (or edges). An arc is a line that joins one node to another. Arcs can be directed (in which case you can only travel in one direction along them) or undirected.
A connected graph is defined as a graph where you can get from any one node to any other node by travelling along some arcs (possibly via many other nodes).
A cycle is a set of arcs that will take you from one starting node to some other nodes and back to the starting node without ever travelling along the same arc twice. It's a loop, if you like.
An acyclic graph has no cycles.
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