User:Mpagey/Padmakar-Ivan Index

Consider a graph, $$G$$, such that the edge connecting any two given points, $$u$$ and $$v$$, in $$G$$ is denoted as $$e$$. Let $$n_{eu}(e|G)$$ represent the number of edges of $$G$$ that are closer to point $$u$$ than point $$v$$. Similarly, let $$n_{ev}(e|G)$$ represent the number of edges of $$G$$ that are closer to $$v$$ than $$u$$. In this case, the Padmakar-Ivan Index of the graph $$G$$, $$PI(G)$$, is defined as: $$PI(G) = \sum_{\forall{e}}\left( n_{eu}(e|G) + n_{ev}(e|G) \right)$$