To determine if a graph is connected, one can use standard search algorithms like Breadth-First Search (BFS) or Depth-First Search (DFS). Start the search from any node and track the visited nodes throughout the process. After the search completes, check for any unvisited nodes; if any exist, the graph is not connected. If all nodes are visited, the graph is confirmed to be connected. This method provides a practical approach to assessing graph connectivity.