The Euler characteristic χ = |V |−|E| is an important topological characteristic of graphs and networks. Here, |V | and |E| denote the number of vertices and edges of a graph or a network. It has been shown in [Phys. Rev. E 101, 052320 (2020)] that the Euler characteristic can be determined from a finite sequence of the lowest eigenenergies λ1, . . . , λN of a simple quantum graph. We will test this finding numerically, using chaotic graphs with |V | = 8 vertices. We will consider complete

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... y connected) and incomplete realizations of 8-vertex graphs. The properties of the Euler characteristic will also be tested experimentally using the sequence of the lowest resonances of the 5-vertex microwave network. We will show that the Euler characteristic χ can be used to reveal whether the graph is planar or not. topics: quantum graphs, microwave networks, Euler characteristic