This Analysis: Modularity Analysis is Using OpenRank on Farcaster Social Graph for Optimism Citizens and Guest Voters
OpenRank Farcaster Social Graph:
OpenRank is a decentralized ranking and reputation protocol. It enables a verifiable reputation compute layer for the open web that unlocks a broad range of useful applications, including those that resist cryptographic or game-theoretic mechanisms of trust. Using graph compute algorithms like EigenTrust, it offers resilience from sybil contexts, provides scalable and context-specific compute, and enables permissionless access to compute and reputation data for any developer.
Algorithm and Ranking Strategy is Based on Network Engagement Global Profile Ranking | OpenRank
Approach 1: OpenRank Farcaster Network EigenTrust Visualization Exercise:
https://hub.graphistry.com/graph/graph.html?dataset=f9e51a6e9b5d41debcb495bb16b05012
Blue = citizens
Pink = Guests
Right now the label on the node is 1 or 2 and you need to click on it to know which is the username on that node
Approach 2: Personalized Farcaster Network Analysis:
- Run EigenTrust using OpenRank for each person individually to generate a ranked list of their trusted peers
- Adds an additional dimension by looking not just at follows but also the interactions that people have
- Identify the degree of overlap between the lists to find whether members belong to similar social groups
Data: we have run personalized EigenTrust for each of the Optimism citizens and guest voters, generate a list of top 100 highest non-zero score peers on the Farcaster social graph.
“source” nodes are Farcaster nodes that are either a citizen or a guest voter.
“target” nodes are the top 100 Farcaster friends of a source node.
“source-target” EigenTrust value shows the trust score from a source to its top 100 targets
Key Findings (approach 2):
Retro 5 Citizens versus Guest Voters
1. Trust Dynamics by Relationship Types
This bar chart visualizes the average EigenTrust scores for different source-target relationships:
- Citizen-to-Citizen Trust:
- Average Trust Score: 0.008731 (Highest among all categories).
- This indicates that citizens generally exhibit stronger trust relationships when interacting with other citizens. This suggests the presence of tighter-knit or more reliable trust dynamics within the citizen community.
- Guest-to-Citizen Trust:
- Average Trust Score: 0.007987 (Second highest).
- Guests display considerable trust toward citizens, potentially reflecting a reliance on or respect for the more established citizen nodes within the network.
- Guest-to-Guest Trust:
- Average Trust Score: 0.006920.
- Guests also demonstrate reasonable trust within their own group. While slightly lower than Guest-to-Citizen trust, it is not significantly weaker, suggesting some cohesion within the guest community.
- Citizen-to-Guest Trust:
- Average Trust Score: 0.004094 (Lowest among all categories).
- Citizens exhibit the least trust toward guests, which may point to a lack of familiarity or perceived unreliability among guest nodes.
Trust Dynamics:
- Strong Citizen Cohesion: Citizens trust other citizens the most, indicating a robust internal network of trust within this group.
- Guest Variability: Guests display more dispersed trust dynamics. They trust citizens slightly more than other guests, suggesting they value the reliability of citizen nodes.
- Citizen-Guest Asymmetry: The low Citizen-to-Guest trust score highlights an asymmetry in trust dynamics. Guests trust citizens more than citizens trust guests.
Implications:
- The network is somewhat stratified, with citizens forming a more cohesive group and guests exhibiting a blend of internal and external trust.
- The asymmetry in Citizen-to-Guest trust could reflect differences in perceived authority, reliability, or reputation within the community.
2. Overlap of Social Circles Between Citizens and Guests
To determine if citizens and guests belong to the same social circles, we analyzed the connections between these groups by examining the overlap in their target nodes (friends) and evaluating whether they frequently interact with the same individuals. The approach is:
- Identify common target nodes shared by citizens and guests.
- Calculate the proportion of overlapping targets relative to the total targets for each group.
The analysis reveals the following about the social circles of citizens and guests:
- Overlap (23.02%):
- Only 23% of target nodes are shared between citizens and guests, indicating a limited overlap in their social circles.
- This suggests that citizens and guests do interact but largely maintain distinct connections.
- Citizen-Only Targets (67.70%):
- A significant portion of target nodes (67.7%) are exclusive to citizens. This reflects a tendency for citizens to operate within their own circles.
- Guest-Only Targets (9.28%):
- Guests have relatively few exclusive connections, which might indicate a smaller or less distinct network compared to citizens.
Conclusion:
Citizens and guests belong to largely separate social circles, with some overlap. Citizens dominate the network in terms of exclusive relationships, while guests show a smaller, less defined network of unique interactions.
3. Network Clustering Analysis
- Community Sizes:
- The largest community (Cluster 0) is significantly larger than the others, indicating a dominant group that integrates a mix of nodes (citizens and guests).
- Smaller communities (Clusters 1-5) represent isolated or niche groups with fewer interactions.
- Citizen and Guest Composition:
- The largest cluster shows a higher proportion of citizens compared to guests, reflecting citizens’ dominance in core social interactions.
- Several smaller clusters consist almost entirely of citizens, showing limited guest integration.
- Proportional Distribution:
- Citizens contribute significantly more to the overall community structure, while guests remain underrepresented or isolated.
Retro 6 Citizens versus Guest Voters
1. Trust Dynamics by Relationship Types
Key Insights
- Asymmetry in Trust:
- Guests appear to trust Citizens more than Citizens trust Guests, reflecting a dynamic where Citizens are viewed as more central or influential.
- Citizens exhibit a higher degree of trust within their own community compared to Guests, potentially due to closer or longer-term relationships.
- Network Integration:
- The presence of trust between Citizens and Guests suggests some level of integration between the groups, though the lower scores compared to intra-community trust indicate room for deeper engagement.
- Community Cohesion:
- Citizens have stronger intra-community trust compared to Guests, highlighting a well-established core network.
2. Overlap of Social Circles Between Citizens and Guests
Overlap of Social Circles Between Citizens and Guests
- Total Social Circles:
- Citizen Targets: 3,264 unique connections.
- Guest Targets: 3,825 unique connections.
- Shared Connections:
- 1,319 targets are shared between Citizens and Guests.
- This represents a significant overlap of trusted connections.
- Jaccard Similarity Index:
- 0.229 (22.9%), indicating that approximately 23% of the combined social circles of Citizens and Guests are shared.
Venn Diagram Insights
- The overlap is substantial but not dominant, suggesting that while there are shared nodes of trust, each group also maintains a significant number of unique connections.
- Citizens and Guests appear to have distinct but interconnected networks, with shared connections possibly acting as “bridges” between the two communities.
3. Network Clustering Analysis
Community Composition Analysis
Here’s an overview of the composition and centrality metrics for the identified communities:
Community Composition
| Community | Citizens | Guests | Total Nodes | Citizens (%) | Guests (%) |
|---|---|---|---|---|---|
| 0 | 15 | 192 | 207 | 7.25% | 92.75% |
| 1 | 29 | 138 | 167 | 17.37% | 82.63% |
| 2 | 30 | 93 | 123 | 24.39% | 75.61% |
| 3 | 0 | 3 | 3 | 0.00% | 100.00% |
- Community 0: Predominantly Guest nodes (92.75%), with a small proportion of Citizens.
- Community 1: A larger share of Citizens (17.37%), though still Guest-dominated.
- Community 2: The most Citizen-inclusive community (24.39%).
- Community 3: Consists entirely of Guests, forming an isolated or highly specialized cluster.
Centrality Metrics
| Community | Most Central Node | Max Degree Centrality |
|---|---|---|
| 0 | jessepollak | 0.383 |
| 1 | phil | 0.297 |
| 2 | cameron | 0.255 |
| 3 | gyges- | 0.036 |
- Community 0 (jessepollak): The most central node with the highest degree centrality across all communities, likely serving as a hub for Guest interactions.
- Community 1 (phil): A central figure connecting nodes in this mixed community.
- Community 2 (cameron): A key influencer in the most Citizen-inclusive cluster.
- Community 3 (gyges-): A minor, isolated cluster with limited connections.
Insights
- Citizen Representation:
- Citizens are more concentrated in Community 2 but are generally a minority across all communities.
- Guests dominate most clusters, particularly Community 0 and Community 3.
- Key Influencers:
- Influential nodes act as hubs and bridges within their respective communities.
- Isolated Community:
- Community 3 is entirely Guest-driven, suggesting a specialized or less integrated group.