  We propose novel recommendation algorithms to improve fairness in networks.
Fairness is measured by how close different nodes are to influencers in the
network. To allow for easy comparison of fairness across graphs of different
sizes, our fairness measure is normalized to the same measure on a synthetic
power-law graph of the same size. We experimented with the Erdos-Renyi and
Barabasi-Albert graphs and found the latter to be more robust in terms of
normalization. In addition to developing a new fairness measure, we propose a
new node recommendation algorithm to increase fairness in networks. Our
algorithm works by recommending a target node based on the number of triangles
between the source and target node with probability P, and with probability
1-P, it introduces weak ties and diversity in the network by recommending nodes
using an importance sampling algorithm. This sampling algorithm is based on a
polynomial function of the degree of the target node and its distance from the
influencer set. Through extensive simulations on three real-world network data
sets and comparing seven different algorithms, we show that the algorithm which
recommends target nodes with probability proportional to the square of the
ratio of the degree of the target node to distance to influencer achieves the
best fairness. We show the robustness of the algorithm to different parameter
choices and provide insights on when to use the different importance sampling
methods based on the structure of the network. We also provide a generalization
of our method for disconnected graphs.
