# LAC - Local Average Connectivity-Based Method

#### Definition

Let N

_{v}be the set of neighbors of node v. The subgraph G[N_{v}] induced by N_{v}is named C_{v}. For a node w in C_{v}, distinguished from its degree deg(ω) in G, its local connectivity in C_{v}is represented as deg^{Cv}(w). It is obvious that each node i in G has only one deg(i), but has different deg^{Cv}(i) with respect to different C_{v}. For each node w∈N_{v}, its local connectivity deg^{Cv}(w) is defined as how many other nodes in C_{v}it connects directly. Then, the local average connectivity of a node v (LAC(v)) is defined as the average local connectivity of its neighbors: LAC(v) of a node v describes how close its neighbors are. Essentiality is, in many cases, a product of complex function rather than an individual protein function. The local average connectivity is such a local metric to determine a protein’s essentiality based on the modular nature of protein essentiality.#### References

- LI, M., WANG, J., CHEN, X., WANG, H. & PAN, Y. 2011. A local average connectivity-based method for identifying essential proteins from the network level. Computational biology and chemistry, 35, 143-150. DOI: 10.1016/j.compbiolchem.2011.04.002