Social network graphs help us understand and analyze interactions within large communities. These graphs, characterized by nodes representing individuals and edges denoting relationships or interactions, reveal intricate patterns of influence and connection. Within such networks, identifying key players—hubs and authorities—is crucial for various applications, from marketing strategies to information dissemination to trust evaluation. 

Likewise, in the context of BUILD, understanding user interactions and nominations, mirrors the properties of social network graphs. Here, hubs—users who initiate numerous connections—and authorities—users who receive many endorsements—helps us to understand which builder is deemed influential and hence likely deemed trustworthy by others. 

However, it is undesirable to reward reciprocation (i.e. I reward you, you reward me) as this turns into a collaboration game rather than expression of the trustworthiness of a builder. Therefore, we believe it makes sense to penalize overly reciprocal behavior. Our algorithm aims to distinguish genuine influence from mere social exchanges, thereby providing a clearer picture of each user's true standing within the network. 

HITS-RP: HITS algorithm with reciprocation penalty

We built a directed graph where nodes represent users and edges represent interactions, with weights corresponding to the strength of these interactions. We then apply the HITS algorithm to compute two numbers for a node. Authorities estimate the node value based on the incoming links. Hubs estimates the node value based on outgoing links. Consequently we analyze the mutual interactions (reciprocations) between users. The reciprocity count for a user is the number of users who have reciprocal interactions with them.

Finally we arrive at a trust score for a given node: 

$trustscore(u)=\frac{α⋅hub(u)+(1−α)}{authority(u)1+reciprocitycount(u)}$

Where:

• α is a parameter that balances the hub and authority scores.

• hub(u) and authority(u) are the hub and authority scores of user u obtained from the HITS algorithm.

• reciprocitycount(u) is the count of mutual reciprocations for user u.

How do we know that it works? 

In order to evaluate the algorithms we relied on labels to see how effective the developed algorithm compared to these. For labels we observed which quantiles users were placed based on their trust score. 

Labels:

• farmer - we curated a list of known farmers which aided the evaluation of the score 

• builders - we manually curated a list of builder deemed trustworthy

• farcaster_power_user - we extracted a list of farcaster power users

• profile_completeness - while far from perfect we created a score on profile completeness (i.e. if they hold a talent passport, farcaster profile and have a dedicated username)
  

While we tested several algorithms (semantic analysis, eigentrust, peertrust, mDC) we found that this implementation performed best. Below you can observe the results. 

From the chart we see that it generally places users showing signs of high trustworthiness in higher quantiles while not overly encouraging farmers. 

Integration of Builder Score 

BUILD operates already with an existing Builder Score, if we wanted to integrate the HITS algorithm with reciprocation penalty we simply would assign a weight to the existing Builder Score and to the developed algorithm. 

Let’s assume we wanted to start conservatively and assign a weight of 0.1 to the developed algorithm. We simply would normalize the existing builder score between 0 and 1 and then normalize the HITS-RP. 

$overall score = 0.9 \times builderscore + 0.1 \times HITSRP$

Given the overall score is already normalized between 0 to 1 we can simply multiply it by the overall budget to calculate the budget distribution for a weekly Build airdrop. 

Big thank you to Thomas Eisermann for his work on this research.