Eccentricity Index Calculator

Formula

The formula to calculate the Eccentricity Index (EI) is:

\[ EI = \sqrt{1 - \left( \frac{b^2}{a^2} \right)} \]

Where:

Eccentricity Index (EI): A mathematical concept used in graph theory and network analysis. It measures the maximum distance from one vertex to all other vertices in a graph, providing an indication of how 'eccentric' or 'outlying' a particular point is within the network. This index can be useful in various fields, including computer science, social network analysis, and transportation planning.
Length of Semi-Major Axis (a): The length of the longest radius of an ellipse.
Length of Semi-Minor Axis (b): The length of the shortest radius of an ellipse.

Let's say the length of the semi-major axis (a) is 10 and the length of the semi-minor axis (b) is 6. Using the formula:

\[ EI = \sqrt{1 - \left( \frac{6^2}{10^2} \right)} \]

We get:

\[ EI \approx 0.80 \]

So, the eccentricity index is approximately 0.80.