Flat Recovery Across All Densities: Edge Utilization Is What Moves
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A controlled, 50-run benchmark published in Towards Data Science on August 18, 2026 delivers an inconvenient result for anyone designing multi-agent systems by instinct: saturating a network with communication pathways does not improve its ability to recover ground-truth information. Across five density levels — 20%, 40%, 60%, 80%, and 100% — information recovery stayed inside a band of roughly 0.924 to 0.976, with no meaningful trend in either direction. For engineers who default to fully connected meshes "because it feels safer," the extra edges are largely decorative.
The experiment, authored by Emmimal P Alexander, runs entirely on Python 3.12, uses no external API calls, and costs $0 to execute. That austerity eliminates the confounds that make most topology comparisons uninterpretable.
Isolating One Variable
Most topology experiments change shape and edge count simultaneously when comparing a chain to a mesh to a fully connected graph. When performance shifts, the cause is indeterminate. This experiment fixes that by locking every structural parameter except relationship density, defined as D = E / (N * (N - 1)) for a directed graph with N nodes and E edges.
Eight agents are used throughout. The topology family is strictly Erdős–Rényi random graphs, with edges sampled uniformly at random until reaching each target density. Any sampled graph that is not strongly connected is rejected and resampled, up to 20,000 attempts — eliminating hidden structural artifacts such as central hubs or star topologies. Each of the five density levels runs 10 independent trials with unique, pre-locked random seeds, for 50 total runs, each under a hard cap of 35 messages.
Agents are not LLM-backed. Each follows a deterministic TF-IDF-based policy: contribute whichever unshared fact is least similar to the current shared state, falling back to the most contextually relevant fact once novel knowledge is exhausted. This trades stochastic behaviour for bit-for-bit reproducibility — a trade-off anyone thinking carefully about what the agentic era demands of data science should weigh explicitly.
The Benchmark Numbers
The primary metric — information recovery — measures the fraction of 17 ground-truth facts from a fixed incident scenario that made it into the network's final shared state. Each of the 8 agents holds a non-overlapping slice; no single agent starts with the complete picture.
| Density | Information Recovery | Relationship Efficiency | Redundancy | Configured Edges | Avg. Used Edges | Avg. Edge Utilization |
|---|---|---|---|---|---|---|
| 20% | 0.959 ± 0.070 | 0.457 ± 0.034 | 0.240 ± 0.019 | 11 | 10.7 | 97.3% ± 6.1% |
| 40% | 0.924 ± 0.083 | 0.440 ± 0.039 | 0.243 ± 0.027 | 22 | 15.8 | 71.8% ± 11.1% |
| 60% | 0.971 ± 0.039 | 0.469 ± 0.019 | 0.240 ± 0.025 | 34 | 21.3 | 62.6% ± 5.4% |
| 80% | 0.976 ± 0.039 | 0.471 ± 0.023 | 0.249 ± 0.019 | 45 | 24.8 | 55.1% ± 7.1% |
| 100% | 0.959 ± 0.046 | 0.463 ± 0.021 | 0.250 ± 0.026 | 56 | 26.4 | 47.1% ± 4.6% |
Recovery and redundancy are both essentially flat. Relationship efficiency — the fraction of messages that added a genuinely new fact to shared state — holds between 0.44 and 0.47 with no directional trend. The 40% condition posts the lowest mean recovery at 0.924, but with 10 trials and visible within-condition variance, the author flags it as a candidate for further testing rather than a confirmed non-linear effect.
Edge Utilization: Where the Real Story Is
The flat recovery curve conceals a sharp underlying divergence. Edge utilization drops monotonically from 97.3% at 20% density to 47.1% at 100% density. At the sparse end, the network uses nearly every pathway it has. At full connectivity, it ignores more than half of what is configured.
The absolute count of active edges still climbs with density, from 10.7 at 20% to 26.4 at 100%, so additional edges are not completely inert. But the marginal return collapses: doubling the edge budget from 60% to 100% increases configured edges from 34 to 56, yet adds only about 5 more active edges in practice (21.3 to 26.4). Configured connectivity and behavioural connectivity are not the same quantity, and they diverge faster as the graph grows denser — a structural analogue to the distinction between four agent control layers and the contracts that actually govern behaviour.
Known Limits and Open Questions
The deterministic agent policy means results reflect a fixed, rational routing strategy rather than a stochastic LLM population. The 35-message budget proved generous for a 17-fact scenario, likely creating a ceiling effect that compressed the room for density to show impact. The dataset corpus rotates only three core incident templates across ten scenario files, limiting semantic variety.
A tighter-budget follow-up run suggested that mid-density networks might lose more ground under severe message constraints than very sparse or very dense ones, but that pattern is unconfirmed and pre-registration is recommended before treating it as a result. The agent interface was deliberately designed to be modular and agent-agnostic, meaning a real LLM can be swapped in to test whether these structural patterns survive model non-determinism — at the cost of the zero-dollar, zero-API-call reproducibility the current suite provides.
The benchmark delivers a precise, bounded result: within this topology family, this agent count, this task, and this communication policy, scaling density from 20% to 100% does not materially alter what the network recovers. What changes is how efficiently it uses what it is given. For engineers picking topologies by gut feel, that is the figure that should shift the decision — not edge count, but edge utilization, and those two figures move in opposite directions as connections are added.