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We discuss a connection between the generalized Euler characteristic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">E</mi><mi>o</mi></msub><mrow><mo>(</mo><mo>|</mo></mrow><msub><mi>V</mi><msub><mi>D</mi><mi>o</mi></msub></msub><mrow><mo>|</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of the original graph which was split at edges into two separate subgraphs and their generalized Euler characteristics <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">E</mi><mi>i</mi></msub><mrow><mo>(</mo><mo>|</mo></mrow><msub><mi>V</mi><msub><mi>D</mi><mi>i</mi></msub></msub><mrow><mo>|</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>V</mi><msub><mi>D</mi><mi>o</mi></msub></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>V</mi><msub><mi>D</mi><mi>i</mi></msub></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> are the numbers of vertices with the Dirichlet boundary conditions in the graphs. Applying microwave networks which simulate quantum graphs, we show that the experimental determination of the generalized Euler characteristics <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">E</mi><mi>o</mi></msub><mrow><mo>(</mo><mo>|</mo></mrow><msub><mi>V</mi><msub><mi>D</mi><mi>o</mi></msub></msub><mrow><mo>|</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">E</mi><mi>i</mi></msub><mrow><mo>(</mo><mo>|</mo></mrow><msub><mi>V</mi><msub><mi>D</mi><mi>i</mi></msub></msub><mrow><mo>|</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></semantics></math></inline-formula> allows finding the number of edges in which the subnetworks were connected.