#### Answer

This graph has neither an Euler path nor an Euler circuit.

#### Work Step by Step

According to Euler's theorem, for a connected graph to have at least one Euler path, the number of odd vertices must be either 0 or 2. For a connected graph to have at least one Euler circuit, the number of odd vertices must be 0.
This connected graph has exactly four odd vertices. Therefore, by Euler's theorem, the graph has neither an Euler path nor an Euler circuit.