A bridge connects the group but does not shorten its endpoints
Suppose A is close to B and B is close to C. That alone does not establish that A is close to C. Angular separation is not transitive. A connected chain and an all-pairs group answer different mathematical questions, even when a reader uses the word stellium for both.
The distinction matters when an app draws a line between nearby planets and then labels the whole connected group. That visual connection may be correct while the stronger claim, every planet is conjunct every other one, is false. You need the pair distances to tell which statement the display supports.
Calculate the three missing comparisons
Take three invented tropical longitudes: A = 122 degrees, B = 128 degrees and C = 134 degrees. They correspond to 2, 8 and 14 degrees Leo. These are abstract test positions, not identified planets in a historical chart. For this demonstration choose an inclusive six-degree orb; six is an example setting, not a universal astrological standard.
A to B is six degrees. B to C is six degrees. A to C is twelve degrees. There are two accepted edges out of three possible pairs. All three points belong to one connected chain because B links the endpoints. The three-point set fails the all-pairs test because twelve is greater than six.
Do not write that the whole configuration is within six degrees. Its end-to-end span is twelve degrees. A precise summary is: three same-sign objects, two pairwise contacts at the selected orb, one connected component, and no three-member all-pairs group.
Change only the orb and watch the result
At an orb of five degrees, neither six-degree contact qualifies, so all three objects are isolated. At six degrees, the chain forms through B. At twelve degrees, the endpoint pair also qualifies and the all-pairs test passes. No position changed during these three checks.
This small sensitivity table is more useful than choosing the result you like best. If one app uses a five-degree allowance and another uses six, their different group labels follow directly from their settings. If both use six but disagree, inspect whether one uses a connected-chain rule and the other requires all pairs.
Equality is another hidden setting. Our test uses separation less than or equal to the orb. Software using strictly less than six would reject contacts exactly at six. With real data, compare unrounded longitudes; a printed 6.0 can conceal values on either side of the cutoff.
Use circular distance at the Aries boundary
For any two longitudes, first take the absolute difference, then choose the smaller of that number and 360 minus that number. That gives the shorter angular separation. It prevents a pair at 359 and 1 degrees from being misread as 358 degrees apart; its shorter separation is two degrees.
This boundary example is separate from the Leo chain. It shows why subtracting printed sign degrees is unsafe across signs. Convert to a consistent zero-to-360 longitude before comparing. A close out-of-sign contact can exist even though a same-sign counting test puts the objects in different bins.
For a larger set, list each unordered pair once. Four members produce six pairs; five produce ten. Draw an edge only when that pair passes the selected orb. A connected path establishes a chain. An all-pairs group requires every possible edge among its members.
Reject the shortcut that a drawn chain proves one tight conjunction
A path across a diagram establishes connectivity under its edge rule. It does not establish a maximum six-degree span or make distant endpoints a close pair. Describing those endpoints as directly conjunct would add a relationship the calculation rejected.
Neither mathematical test measures how strongly somebody experiences a chart. The diagram is an audit of positions and a chosen convention. Interpretive traditions can use different orbs and membership rules; record those choices rather than claiming the graph settled their meaning.
What should I save when two calculators disagree?
Save the positions, included-object list, zodiac frame, orb, inclusive or exclusive boundary, and group rule. A screenshot with only the final stellium badge leaves most of the disagreement unresolved. Reproduce the pair table first; only then compare the group label.
Does our stellium detector certify a conjunction chain? No. It reports its documented sign and house counts and degree information. Use the pairwise method here for the separate orb question. Do not reinterpret a sign-count result as certification that every pair is conjunct.
Sources and original contribution
Tarot.com’s stellium overview provides the broader grouping context. The explicit pair matrix, graph distinction, orb sensitivity experiment and circular-boundary test on this page are original mathematical demonstrations, not quotations or claims of an observed natal chart.