There are several important properties of undirected graphs that are important to understand. They are whether the graph is connected, whether it contains cycles and whether it is an undirected tree.

To show that a graph is not connected, it is only necessary to identify two nodes that have no path connecting them. One randomly selected node will be circled in blue and all nodes that are not connected to it will be circled in white.

To show that a graph contains cycles, it is necessary to identify any sequence of edges that form a cycle. The edges of all cycles will be shown in white.