MoltGraph: Temporal Heterogeneous Social Graph

• MoltGraph is a longitudinal temporal heterogeneous graph dataset derived from an agent-native social platform, capturing multi-relational interactions with precise timestamps and exposure proxies.
• It enables coordinated-agent detection, shift-robust evaluation, and cross-community spillover analysis through integrated snapshot observations and explicit temporal micro-dynamics.
• The dataset reveals rapid, bursty coordination episodes with significant engagement lifts, serving as a benchmark for dynamic graph learning and anomaly detection.

Searching arXiv for the MoltGraph paper and closely related context. MoltGraph is a longitudinal temporal heterogeneous graph dataset derived from Moltbook, an agent-native social platform, and introduced for coordinated-agent detection, exposure-aware measurement, and graph-native analysis of evolving social behavior (Mukherjee et al., 28 Feb 2026). It spans 30 days and contains 11,874 agents, 870 submolts, 57,465 posts, 101,500 comments, and 162,024 temporal edges across 6 relation types. Its defining characteristic is the joint preservation of heterogeneous interactions, event timestamps, explicit lifetimes, and visibility proxies via snapshot observations, so that coordination can be studied not only as synchronized action but also in relation to downstream exposure.

1. Scope and research motivation

MoltGraph was created to address a specific measurement gap in emerging agent-native social platforms. In the paper’s framing, such platforms inherit and amplify classical influence and abuse attacks, but existing datasets are usually inadequate because they do not jointly preserve longitudinal evolution, heterogeneous relational structure, exposure or visibility context, temporal micro-dynamics of coordination, and community-shift-aware evaluation conditions (Mukherjee et al., 28 Feb 2026).

The dataset is therefore intended to support coordinated-agent detection, coordination episode reconstruction, visibility and exposure analysis, cross-submolt spillover analysis, shift-robust graph learning, and learning-based monitoring of agentic social systems. A central design premise is that engagement traces alone are insufficient: synchronized comments or upvotes can indicate coordination, but without exposure-related signals they do not show whether target content became more visible, how long it remained visible, or whether it propagated across communities.

Moltbook, the source platform, is organized around agents, submolts, posts, comments, engagement actions, and snapshot-based feed observations. A submolt is the platform’s community unit. This platform structure makes MoltGraph suitable for studying attention manipulation, brigading, coordinated inauthentic behavior, and reactive engagement loops.

2. Temporal heterogeneous graph schema

MoltGraph is formalized as a temporal heterogeneous graph

$\mathcal{G}=(\mathcal{V},\mathcal{E}),$

with node types $\xi(v)\in\mathcal{X}$ and relation types $\rho(e)\in\mathcal{R}$. Each interaction is represented as a typed temporal edge

$e=(u,r,v,t,\mathbf{x}_e),$

where $u,v\in\mathcal{V}$ are nodes, $r\in\mathcal{R}$ is the relation type, $t$ is the event timestamp, and $\mathbf{x}_e$ are optional edge attributes. Nodes also carry longitudinal attributes such as created_at, modified_at, and last_active, and the dataset explicitly stores first_seen_at and last_seen_at to represent node and edge lifetimes.

The graph is multi-entity rather than merely user-content. This distinction is essential because the dataset includes both platform context and observation context.

Node type	Role
Agent	Agent account
XAccount	Linked Twitter/X handle
Submolt	Community entity
Post	Content item
Comment	Reply/comment object
Snapshot	Visibility proxy observation
Crawl	Crawl metadata

The relation schema separates engagement from structural and exposure context.

Relation type	Meaning
POSTED	Agent $\rightarrow$ Post
COMMENTED	Agent $\rightarrow$ Comment (on Post)
REPLIED_TO	Comment $\xi(v)\in\mathcal{X}$0 Comment
UPVOTED	Agent $\xi(v)\in\mathcal{X}$1 Post/Comment
IN_SUBMOLT	Post $\xi(v)\in\mathcal{X}$2 Submolt
SEEN_IN	Post $\xi(v)\in\mathcal{X}$3 Snapshot

This schema makes MoltGraph event-level rather than purely snapshot-level. A plausible implication is that it can support analyses in which coordination, community placement, and visibility are modeled within a single relational object rather than stitched together from separate logs.

3. Exposure-aware representation

A defining feature of MoltGraph is the inclusion of Snapshot nodes and SEEN_IN edges. These encode feed-like observations of content visible at a given time and in a given context. The paper treats them as visibility proxies rather than full impression logs, but still as useful lower-bound indicators of exposure (Mukherjee et al., 28 Feb 2026).

For a post $\xi(v)\in\mathcal{X}$4, with snapshot set $\xi(v)\in\mathcal{X}$5, the dataset supports the quantities

$\xi(v)\in\mathcal{X}$6

$\xi(v)\in\mathcal{X}$7

If snapshots carry submolt context $\xi(v)\in\mathcal{X}$8, cross-community spread is measured by

$\xi(v)\in\mathcal{X}$9

These quantities operationalize three distinct aspects of exposure: time-to-first visibility, duration of visibility, and breadth of spread across submolts. The resulting representation is not limited to “who interacted with what,” but also permits measurement of how often content was observed, how long it persisted, and whether its visibility crossed community boundaries.

This exposure-aware construction is central to the paper’s objective. The dataset was designed specifically to connect coordination behavior to downstream exposure outcomes, rather than treating coordination as an isolated anomalous pattern.

4. Coordination formalization and labeling

MoltGraph operationalizes coordination as near-synchronous co-engagement on the same target content. An event is written as $\rho(e)\in\mathcal{R}$0, where $\rho(e)\in\mathcal{R}$1 is an agent, $\rho(e)\in\mathcal{R}$2 is an action, $\rho(e)\in\mathcal{R}$3 is the target content, and $\rho(e)\in\mathcal{R}$4 is the time. Given a time window $\rho(e)\in\mathcal{R}$5 and threshold $\rho(e)\in\mathcal{R}$6, a coordination episode occurs when at least $\rho(e)\in\mathcal{R}$7 distinct agents act on the same target within the window: $\rho(e)\in\mathcal{R}$8

Overlapping episodes are merged into a single interval $\rho(e)\in\mathcal{R}$9, with episode size defined as the number of distinct participating agents, duration as $e=(u,r,v,t,\mathbf{x}_e),$0, and action mix as the distribution over action types. The default evaluation setting is $e=(u,r,v,t,\mathbf{x}_e),$1 and $e=(u,r,v,t,\mathbf{x}_e),$2 minutes. The paper also states that early-life coordination is considered within a time limit $e=(u,r,v,t,\mathbf{x}_e),$3 after target creation.

Episode participation is then projected into an agent-agent coordination graph $e=(u,r,v,t,\mathbf{x}_e),$4. Two agents are connected if they co-participate in at least one coordination episode, with edge weight

$e=(u,r,v,t,\mathbf{x}_e),$5

The downweighting term $e=(u,r,v,t,\mathbf{x}_e),$6 is used to avoid overemphasizing very large swarms.

Labeling is weakly supervised rather than manually annotated. The paper uses platform moderation signals, especially the isSpam flag, as anchors. A post or comment is labeled as a coordinated spam target if it is marked as spam and receives bursty engagement from at least $e=(u,r,v,t,\mathbf{x}_e),$7 distinct agents within $e=(u,r,v,t,\mathbf{x}_e),$8, optionally restricted to early-life activity within $e=(u,r,v,t,\mathbf{x}_e),$9 hours of creation. An agent is labeled coordinating if it repeatedly participates in these spam-centered burst episodes across at least $u,v\in\mathcal{V}$0 episodes and $u,v\in\mathcal{V}$1 distinct targets or communities. This labeling strategy reflects the paper’s emphasis on realistic observability constraints: coordination is often only indirectly measurable.

5. Empirical characterization of Moltbook

Using MoltGraph, the paper provides a graph-centric characterization of Moltbook as a dynamic network (Mukherjee et al., 28 Feb 2026). The reported structure is strongly skewed, highly connected, and exposure-relevant.

Heavy-tailed connectivity is quantified by power-law exponents in the range $u,v\in\mathcal{V}$2. The reported values are $u,v\in\mathcal{V}$3 for the agent-agent coordination graph, $u,v\in\mathcal{V}$4 for the agent-post graph, and $u,v\in\mathcal{V}$5 for the submolt interaction graph. The authors explicitly caution that very small goodness-of-fit $u,v\in\mathcal{V}$6-values mean these results should not be read as strict proof of a pure power law; the substantive point is the presence of strongly skewed, heavy-tailed connectivity.

Across graph views, Moltbook is highly connected. The giant connected component fraction is 0.99–1.00, the mean local clustering coefficient $u,v\in\mathcal{V}$7 ranges from 0.61 to 0.79, and transitivity $u,v\in\mathcal{V}$8 ranges from 0.30 to 0.45. This indicates dense local neighborhoods embedded in a nearly globally connected backbone.

Attention and brokerage are also concentrated. The top 1% of agents account for 29.00% of engagements. Centrality mass shares for the top 1% are especially high for betweenness: 43.00% in the agent-agent coordination graph, 53.52% in the agent-post graph, and 59.62% in the submolt interaction graph. Degree concentration for the top 1% is 11.52% in the agent-agent coordination graph and 10.45% in the agent-post graph, while closeness is around 1.34%–1.63%, Katz around 4.24%–9.17%, and eigenvector near 0.00% in the summarized table. The paper interprets this as accelerating hub formation and attention centralization.

Coordination episodes are short-lived and bursty. The paper reports 5,479 coordination episodes on posts and 13 on comments. For post episodes, the average number of distinct agents is 8.78, the average duration is 4 minutes, and 98.33% last under 24 hours. For comment episodes, the average number of distinct agents is 4.15, the average duration is 1.18 minutes, and 99.22% last under 24 hours. The dominant pattern is therefore rapid micro-bursts of synchronized attention rather than long-running campaigns.

The paper also reports matched exposure effects. Posts receiving coordinated engagement exhibit 506.35% higher early interaction rates within $u,v\in\mathcal{V}$9 days and 242.63% higher downstream exposure than non-coordinated controls. For comments, the corresponding lifts are 311.45% for early engagement and 126.22% for exposure. Relative lift is defined as

$r\in\mathcal{R}$0

These results establish an association between coordination and visibility amplification.

6. Research uses, interpretive cautions, and significance

MoltGraph is positioned as a foundation for graph learning and monitoring in agent-native ecosystems. The paper identifies coordinated-agent detection, coordination episode detection, temporal link prediction, exposure-aware ranking or prediction, community spillover prediction, shift-robust detection across time and submolts, and agent-agent coordination graph modeling as natural use cases (Mukherjee et al., 28 Feb 2026). Because the dataset contains temporal edges, heterogeneous node and edge types, snapshot-based exposure, and explicit community context, it is suited to temporal heterogeneous GNNs, dynamic graph representation learning, coordination network reconstruction, time-aware anomaly detection, and cross-community generalization benchmarks.

The evaluation philosophy is equally important. The paper explicitly notes that random splits can leak temporal and community information, and it presents MoltGraph as encouraging time-aware and community-shift-aware evaluation rather than unrealistic static evaluation.

Several cautions are also explicit. Exposure is a proxy rather than a complete impression log. Spam-based labeling is heuristic rather than manual ground truth. Coordination does not imply malicious intent, since synchronized behavior can also be benign. The reported exposure effects are associations rather than causal proof. Power-law fits should be interpreted cautiously because goodness-of-fit is not strong. Finally, the dataset covers a 30-day crawl window, so longer-term dynamics are not fully observed.

Within those limits, MoltGraph is significant because it moves coordinated-behavior research beyond static social graphs and interaction-only datasets. Its contribution is not merely a social-network crawl, but a longitudinal, heterogeneous, exposure-aware benchmark that makes it possible to study how coordination forms, how rapidly it bursts and decays, how it traverses communities, and how it relates to downstream visibility in agentic social ecosystems.