# SocialRank

SocialRank is an approach to assess the relevance of a person in a community. The basis for the calculation is the mapping of the underlying social structure as a social network that models members (nodes) and their relationships to one another (edges) as a graph . The SocialRank then assigns a numerical weighting to each node in order to express the relative importance or influence of this node or this person in the network.

One approach to calculating the SocialRank is to superimpose the attention that the respective person receives and the SocialRank of their neighbors in the network. This is defined analogously to Google's PageRank algorithm:

${\ displaystyle SR (P_ {i}) = (1-d) A_ {i} + d \ left ({\ frac {SR (P_ {1})} {C (P_ {1})}} + \ dots + {\ frac {SR (P_ {n})} {C (P_ {n})}} \ right)}$

With

• ${\ displaystyle SR (P_ {i})}$ is the SocialRank of the individual ${\ displaystyle P_ {i}}$
• ${\ displaystyle P_ {i}}$is an individual who has a relationship with${\ displaystyle P_ {1}, \ dots, P_ {n}}$
• ${\ displaystyle C (P_ {i})}$is the total number of all contacts that has${\ displaystyle P_ {i}}$${\ displaystyle C (P_ {i}) \ geq 1}$
• ${\ displaystyle d}$ is a weighting factor with ${\ displaystyle 0 \ leq d \ leq 1}$
• ${\ displaystyle A_ {i}}$is the direct attention that receives from the community${\ displaystyle P_ {i}}$

SocialRank is useful for describing communication networks such as e-mail or instant messaging, but it is particularly suitable for analyzing users of Web 2.0 services such as B. Contact management portals.