In graph theory, a Cactus is a connected graph such that any distinct two simple cycles in the graph share at most one vertex.
Here is a Cactus with 3 simple cycles outlined with dashed lines.
The following graph is similar to the one pictured above but is not a Cactus because the two vertices labeled in red are shared by two simple cycles.
Things can get a little bit trickier, for example the following graph:
Might look like a Cactus but it is not. This can be shown by highlighting the following cycle:
This cycle shares more than one point with a lot of the more obvious cycles in the graph.
A connected graph is a graph such that there exists at least one path between any two vertices.
A simple cycle is a path on a graph that starts and ends at the same vertex and visits no vertex more than once.
A simple graph is an undirected, unweighted graph such that no vertices are connected two each other by more than one edge and no vertex is connected to itself. A simple graph is the most basic type of graph and is what most people mean when they say graph.
Take a simple graph as input and decide whether it is a Cactus graph. You should output two distinct values one for True and one for False. You may take input in any format you see fit.
This is code-golf so you should aim to minimize the byte count of your answers.