CollegeMsg tie structure¶

CollegeMsg can test whether observable communication intensity aligns with local overlap and global connectivity without treating messages as friendship.

Measurement contract¶

directed timestamped messages                     source truth
              |
              v
final simple undirected contact graph              explicit projection
              |
       +------+------+----------------+
       |             |                |
       v             v                v
message count    active days      reciprocity       separate strength views
       |             |                |
       +------+------+----------------+
              |
       +------+----------------+
       |                       |
       v                       v
neighborhood overlap      edge-removal curves       descriptive measurements

Self-messages do not create contacts. For every contacted pair, message count includes all non-self messages, active days counts distinct UTC Unix days, and reciprocity records whether at least one message occurred in each direction. None is called a friendship or combined into an invented strength score.

Neighborhood overlap is the shared-neighbor count divided by the union of the endpoints' neighbors after excluding the endpoints. An isolated dyad has no defined denominator and remains explicitly unavailable. Embeddedness is the shared-neighbor count; zero identifies a local bridge in the final simple graph.

Message count and active days use fixed power-of-two bins. Reciprocity remains a two-category view. The experiment removes edges in ascending and descending order for each view, shuffling ties with the configured seed before stable sorting. A separately shuffled order supplies the deterministic random baseline. Every ten percent it reports all components and the largest component over the stable 1,899-node universe, including isolates.

Observation¶

Revision b41c318 produced this CPU witness in 1.347 seconds:

uv run --locked python -m experiments.run college_msg_ties SEED=0

The 59,835 messages contain no self-message, project to 13,838 contacted pairs, and include 6,458 reciprocal pairs. The final graph has four components; its largest contains 1,893 of 1,899 nodes. Of all contacts, 3,969 are local bridges and three isolated-dyad overlaps are unavailable.

Message count aligns monotonically with greater mean overlap across every observed bin:

The active-day view rises from 0.026577 mean overlap for 8,725 one-day ties to 0.040628 for 236 ties active on 8-15 days. The two higher bins contain only 35 and 7 ties and are not monotone, so they do not support a stronger trend claim. Reciprocal contacts have 0.032750 mean overlap and 3.399 mean embeddedness, versus 0.025375 and 2.846 for one-way contacts. Local bridges are 23.5% of reciprocal contacts and 33.2% of one-way contacts.

Weak-first removal consistently reduces the giant component more than strong-first removal. The random column is one common seed-zero baseline; the mean is the arithmetic mean of largest-component fractions at the eleven ten-percent checkpoints, including zero and complete removal.

Two clean sensitivity runs at revision e05b08d changed both the within-strength tie order and random baseline:

uv run --locked python -m experiments.run college_msg_ties SEED=1
uv run --locked python -m experiments.run college_msg_ties SEED=2

Across all three seeds, message-count weak-first means span 0.6347-0.6369 versus 0.8011-0.8024 strong-first; active-day means span 0.6845-0.6880 versus 0.7738-0.7803; and reciprocity means span 0.6750-0.6768 versus 0.7787-0.7816. The random means span 0.7367-0.7447. The ordering therefore survives this bounded sensitivity check, though three seeds do not remove the projection confounders.

For reciprocity, weak-first removes one-way contacts before reciprocal contacts; strong-first reverses that order. These curves support the descriptive weak-tie pattern in this projection. They do not estimate what would happen if social relationships were removed: activity, degree, homophily, observation coverage, and within-bin ordering remain confounded, and the final graph uses the complete observation period.

Decision¶

The projection, strength policies, overlap, and connectivity measurements remain research-only. TemporalEdges and college_msg() already own the reusable event and source facts; no Graph method, automatic snapshot, community API, or analytics dependency follows from this experiment.

The evidence closes this final-graph stage. A temporal bridge-lifecycle study would require a new contract over strict prefixes; it should not reuse these complete-period measurements as if they were available earlier.