## Alternatives to Graph theory?

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• I was planning to use a graph theoretic and page-rank approach to finding the most influential person in an organization.

Influential person is someone who drives a lot of activity in the organization. When he assigns a task, most people do it. When he sends a mail, most people reply to him. When he assigns some training, most people do it.

But there is one drawback to using graph theory here. For example, say Person A is very influential, and Person B has just joined an organization and works under A. B puts in a leave request and sends it A for approval. A approves the leave request. This seems contradictory, since A is very influential but A responded to B. According to graph theory, wouldn't this make Person B also very influential? This approach would give very bad results.

How can i overcome this limitation? Can anyone suggest an alternative approach?

• I am using number of interactions to calculate an affinity scores between two users. Based on this, I suggest what content should be shown to a user (like FaceBook does). User A responds to User B most of the time. so (A->B) has a high affinity score. So, in user B's newsfeed I intend to show content coming from User A.

is there a better way than just counting number of interactions?

If two users A & C have same affinity scores with B, if A is more influential than B, A's content will be shown first to user B.

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## According to graph theory, wouldn't this make Person B also very influential?

No. You need to think about how to set up your graph first and then go further. In this case your graph is not simple but both weighted and directed thus handling a request of B by A neither reduces A's influence nor improves B's. Because the weights of directed edges are determining the influence.

## Is there a better way than just counting number of interactions?

Community Detection or what computer scientists call Graph Clustering. If you do not have to limit yourself to hierarchies, you can extract communities who have the most interaction and share suggestions inside the community.

In a weighted and directed graph, what is the best measure of Influence? Eigen centrality, Betweeness Centrality or Weighted Avg. Degress, In-Degree – None – 2016-01-05T05:47:34.743

All centrality measures are actually talking about the same concept but with different languages. The best is to take a sample data and see which one works better for your purpose. Please note that 1) Not all of them have a wighted directed version and 2) If your graph is big then the computational complexity matters a lot (e.g. Eigen centrality is not comfortable for gigantic graphs) – Kasra Manshaei – 2016-01-05T08:20:58.043