# Weighted LeaderRank

#### Definition

Weighted LeaderRank is a variant to LeaderRank via assigning degree-dependent weights onto links
associated with the ground node.

If network is described by an (N+1)-dimensional weighted adjacency matrix W, so: (i) if a

If network is described by an (N+1)-dimensional weighted adjacency matrix W, so: (i) if a

_{ij}= 0, then w_{ij}= 0; (ii) for any normal node i and the ground node g, w_{gi}= (k^{in}_{i}) and w_{ig}= 1, where is a free parameter; (iii) for all other cases, w_{ij}= 1. After determining the weight of every link, the dynamics follows a biased random walk, namely the score from node j to node i is proportional to the weight w_{ji}: Same to LeaderRank, use final scores in the steady state to quantify nodes’ influences.**See also LeaderRank**#### Software

#### References

- LI, Q., ZHOU, T., LÜ, L. & CHEN, D. 2014. Identifying influential spreaders by weighted LeaderRank. Physica A: Statistical Mechanics and its Applications, 404, 47-55. DOI: 10.1016/j.physa.2014.02.041