If you visit https://github.com/Stellarium/stellarium/tree/master/skycultures you see several sky cultures that include various constellation shapes (you also get this directory when you download stellarium).
As an example, lets look at https://github.com/Stellarium/stellarium/tree/master/skycultures/western_rey, in particular the file https://github.com/Stellarium/stellarium/blob/master/skycultures/western_rey/constellationship.fab and line number 127 which reads:
Aql 10 98036 97649 97649 97278 97278 96229 96229 95501 95501 97804 99473 97804 95501 93747 93747 93244 95501 93805 93805 93429
The "Aql" stands for the for the constellation Aquila, the Eagle (https://github.com/Stellarium/stellarium/blob/master/skycultures/western_rey/constellation_names.eng.fab verifies this)
The "10" means there are 10 lines that make up the markings for Aquila. Note that these lines are specific to the H.A. Rey skyculture. Different cultures will have different lines.
The next 20 number represent the lines themselves. For example "98036 97649" is a line from star 98036 to star 97649, and "97649 97278" is a line from star 97649 to star 97278. Since these two lines share star 97649, they are connected, but that's not always the case with adjacent lines. For example "95501 97804 99473 97804" represents a line from star 95501 to star 97804 and another unconnected line from star 99473 to star 97804.
The next question: what exactly IS star 98036?
If you look at https://github.com/Stellarium/stellarium/blob/master/stars/default/name.fab you'll see it's Beta Aquilae, but not all stars have names in this file, and the name isn't particularly helpful in finding the star itself.
Stellarium itself stores this data in the "catalog files" at https://github.com/Stellarium/stellarium/tree/master/stars/default with the format described at http://stellarium.sourceforge.net/wiki/index.php/Star_Catalogue_Format
However, this can be ugly. Since Stellarium uses the standard Hipparcos catalog, you can visit ftp://cdsarc.u-strasbg.fr/pub/cats/I/239/ and download "hip_main.dat.gz". The format is described at http://cdsarc.u-strasbg.fr/viz-bin/Cat?I/239
The line relating to star 98036 starts:
H| 98036| |19 55 18.77|+06 24 28.6| 3.71|...
which tells us star 98036 is at J2000 right ascension 19h55m18.77s, declination +06 degrees, 24'28.6" declination, and has a magnitude of 3.71. This agrees almost perfectly with https://en.wikipedia.org/wiki/Beta_Aquilae (the declination is slightly off, but this may be because Beta Aquilae is a double star, and Hipparcos references the brighter star and Wikipedia references the midpoint of the double star-- or something).
There are other files in the stellarium github (eg, culture-specific star names) that also use the Hipparcos numbering designation.