# LTR - Linear Threshold Rank

#### Definition

Linear Threshold Rank (LTR) is a new centrality measure based on the linear threshold model, which is defined for each actor as the number of nodes that can be spread when he/she forms an initial activation with his/her neighbors. Linear Threshold Rank defined as fallows:

$$LTR(i)={|f(\{i\} \cup neighbors (i ))| \over n}$$

were $neighbors(i)= \{j \in V |(i,j) \in E \vee (j,i)\in E \}$. And $f$ is a labeling function that quantifies how easily influenceable each actor is. An actor $i \in V$ exerts influence over another actor $j \in V$ if and only if $( i, j ) \in E$. $V$ is the set of actors and $E$ is the set of edges of graph $G$.

Totally it determines to what extent the entire network has a centralized structure

$$LTR(i)={|f(\{i\} \cup neighbors (i ))| \over n}$$

were $neighbors(i)= \{j \in V |(i,j) \in E \vee (j,i)\in E \}$. And $f$ is a labeling function that quantifies how easily influenceable each actor is. An actor $i \in V$ exerts influence over another actor $j \in V$ if and only if $( i, j ) \in E$. $V$ is the set of actors and $E$ is the set of edges of graph $G$.

Totally it determines to what extent the entire network has a centralized structure

#### References

- Riquelme F., Gonzalez-Cantergiani P., Molinero X., Serna M., 2018. Centrality measure in social networks based on linear threshold model. Knowledge-Based Systems, 140, pp.92-102. DOI: 10.1016/j.knosys.2017.10.029