# LID - Local Interaction Density

#### Definition

LID takes the essentiality of a node from interaction densities among its neighbors through topological analyse s of real proteins in a protein complex set first time at the viewpoint of biological modules. The local interaction density of a node $u$ $(LID(u))$ is defined as the density of interactions among its interactive neighbors:

$$LID(u)={|E_{NB\_INT}(u)|\over |V_{NB\_INT}(u)|}$$

Given $G_NB(u)=(V_{NB}(u)),E_{NB}(u))$ be the adjacency subgraph of a protein $u$, called a source node of $G_{NB}(u)$ in a PIN, where $V_{NB}(u)$ is the neighbor node set of source node $u$, and $E_{NB}(u)$ is the edge set in $G_{NB}(u)$.