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Prompt me to enter data to use for the following equation

The provided equation for $\alpha_{\text{metric}}$ is:

\[
\alpha_{\text{metric}} = 1 - \frac{D_o}{D_e} = 1 - \frac{\sum_{v=1, v'=1}^{V} o_{vv'} \delta_{\text{metric}}(v, v')}{\frac{1}{n-1} \sum_{v=1, v'=1}^{V} n_v n_{v'} \delta_{\text{metric}}(v, v')}
\]

To use this equation, we need the following dataThe provided equation for $\alpha_{\text{metric}}$ is:

\[
\alpha_{\text{metric}} = 1 - \frac{D_o}{D_e} = 1 - \frac{\sum_{v=1, v'=1}^{V} o_{vv'} \delta_{\text{metric}}(v, v')}{\frac{1}{n-1} \sum_{v=1, v'=1}^{V} n_v n_{v'} \delta_{\text{metric}}(v, v')}
\]

To use this equation, we need the following 

1. $V$: The number of elements (vertices, nodes, etc.).
2. $o_{vv'}$: Observed metric value between elements $v$ and $v'$.
3. $n$: The total number of observations.
4. $n_v$: The number of occurrences of element $v$.
5. $\delta_{\text{metric}}(v, v')$: The metric distance between elements $v$ and $v'$.

Please provide the values for:

1. The number of elements $V$.
2. The observed metric values $o_{vv'}$ in a matrix form or a list of tuples with the values.
3. The total number of observations $n$.
4. The number of occurrences $n_v$ for each element $v$.
5. The metric distances $\delta_{\text{metric}}(v, v')$ in a matrix form or a list of tuples with the values.

Once you provide these details, I can help you calculate $\alpha_{\text{metric}}$.

Would you like to proceed with any details or have any questions? Here are 5 questions to guide your input:

1. What is the total number of elements (vertices, nodes, etc.) $V$?
2. Can you provide the observed metric values $o_{vv'}$ in a matrix or list form?
3. What is the total number of observations $n$?
4. Can you provide the number of occurrences $n_v$ for each element $v$?
5. Can you provide the metric distances $\delta_{\text{metric}}(v, v')$ in a matrix or list form?

**Tip:** Organizing your data in a clear tabular or matrix format can help ensure accuracy when inputting values.

Learn how to calculate the alpha metric using the provided equation $\alpha_{\text{metric}} = 1 - \frac{D_o}{D_e}$. This involves matrix operations, graph theory concepts, and understanding of linear algebra. Suitable for advanced mathematics.

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