From the provided image, it seems that the graph is drawn as a set of vertices (labeled $A, B, C, D, E, F$) and edges connecting some of them. To determine if the graph is connected:

A graph is connected if there is a path between any two vertices.

Observations:

1. $A, B, C, D$ are connected through edges.
2. $E$ and $F$ appear to be connected only to each other and have no edges linking them to the rest of the graph ($A, B, C, D$).

Conclusion:

This graph is not connected because there is no path connecting $E$ or $F$ to any of the vertices $A, B, C, D$. The graph can be described as having two disconnected components.

Would you like a detailed breakdown of connected components or further clarification?

Expanding Questions:

1. What defines a connected graph in mathematical terms?
2. How can you determine connected components in a disconnected graph?
3. What are the differences between connected, strongly connected, and weakly connected graphs?
4. How does adding edges $E$ or $F$ to the rest of the graph affect connectivity?
5. Can this graph be made Eulerian (having a trail through all edges)?

Tip:

To check connectivity in larger graphs, graph traversal algorithms like Depth-First Search (DFS) or Breadth-First Search (BFS) can be used effectively.