This thesis introduces the concept of Fairness Aware Influence (FAI), which is dependent on prevalence and fairness. Prevalence of a given seed node is the number of infected nodes. Fairness can be defined differently based on the application or problem statement. In this case, the fairness is defined as the variation in the fraction of infections in all the communities. This variation is measured using standard deviation (SD). A lower SD corresponds to better fairness. FAI for a given seed node is defined as the ratio of prevalence to fairness, where a higher FAI score corresponds to higher prevalence and lower SD.

The primary objective of this thesis is to study how network properties such as degree and community size, relate with FAI. Network properties are measured using centrality metrics, which are categorized into two types.
The first type, referred to as "simple" or classic centrality metrics, do not account for community information. The second type, known as community-aware centrality metrics, incorporate community information but were not originally designed for FAI. These serve as baselines for ranking nodes in terms of FAI. Thus, two new classes of metrics are designed specifically for FAI in the attempt to perform better than the baselines.

Six real world networks are employed to evaluate the metrics. Local centrality and Community-Hub-Bridge are found to be good baselines in their respective categories, and the newly proposed metrics surpass the existing ones at the epidemic threshold. Additionally, a discussion is presented to compare and analyze these metrics, considering their performance under varying infection rates using an SIR infection spreading model.