Modeling User Relationships and Information Propagation on Weibo

Unlike traditional internet media, Weibo as a social platform introduces non‑reciprocal user relationships that form a social graph where information spreads from a node through edges to other nodes.

Figure 1 Social graph in Weibo

The breadth and depth of information flow depend on the originator, the intermediate nodes that forward the content, the strength of relationships between nodes, and the community structures they belong to.

Building a user‑relationship model involves analyzing nodes (users), edges (relationships and direction), and relationship circles (clusters) to fully describe the network.

Weibo User Relationship Model

2.1 Quantifying Node Propagation Ability: Propagation Power

Propagation power measures how much influence a user has on information spread; users with larger nodes in the graph have higher propagation power, while smaller nodes have limited impact.

The calculation assumes that propagation power is transmitted in the reverse direction of the information flow, similar to PageRank: a user with high propagation power passes more power to the upstream user when retweeting.

Figure 2 Information propagation path (solid line) & propagation power transmission direction (dashed line)

By collecting a large number of retweet records, a propagation‑power graph is built where nodes are users and edges represent the direction and weight of power transfer; iterative computation continues until values converge.

Figure 3 Propagation‑power transmission graph

2.2 Calculating Edge Strength: Intimacy

Intimacy quantifies the strength of a directed relationship based on interaction behaviors such as comments, retweets, likes, and mentions; the more frequent these actions from user u1 to user u2, the higher the intimacy.

Two additional factors are considered: mutual follows yield higher intimacy than one‑way follows, and highly active users may generate many interactions that do not necessarily indicate strong intimacy, whereas less active users’ interactions can be more reliable.

2.3 Relationship Collaboration: Fan Similarity & Follow Similarity

By treating a user’s follow action as a rating, a user‑by‑user matrix can be constructed where rows represent followers and columns represent followees; binary values indicate whether a follow exists.

Figure 4 User relationship matrix

Computing similarity across rows yields follow similarity (user‑based collaborative filtering), while similarity across columns yields fan similarity (item‑based collaborative filtering); intimacy scores can replace binary entries to reflect weighted relationships.

2.4 Deriving Extended Relationships: Two‑Degree Relationships

Beyond direct (one‑degree) connections, two‑degree relationships are formed via bridge users; the strength of a two‑degree link depends on the number of bridges and the intimacy of the involved edges.

Figure 5 Two‑degree relationship illustration

2.5 Relationship Aggregation: Relationship Circles

Relationship circles are clusters of users with high internal connectivity; they are discovered through a three‑step process.

Step 1: Discover Maximal Cliques – maximal subgraphs where every pair of nodes is connected, representing tightly knit user groups (see Figure 6).

Figure 6 Maximal clique of mutual follows

Step 2: Expand Circles – add new nodes if the increase in internal cohesion outweighs the loss of inter‑circle separation, using a benefit function (illustrated in Figure 7).

Figure 7 A user belonging to two maximal cliques

Step 3: Merge Circles – combine circles with large overlap when the merging improves the overall evaluation function.

3 Summary

Weibo’s social network forms a complex graph with dense and sparse regions; users vary in intimacy with their neighbors, affecting how information propagates.

The presented relationship model captures multiple aspects: propagation power reflects a user’s influence on diffusion; intimacy measures the closeness of two users; fan and follow similarity identify users with shared interests; two‑degree relationships extend direct connections; and relationship circles uncover tightly linked communities, providing a nuanced and comprehensive view of the platform’s social structure.