History: Gismu differing in one letter only

Suppose each of 1342 gismu is represented by a dot (vertex) on a sheet of paper. Now let us connect with a line (link) those gismu which differ only in one letter. The resulting picture is a graph consisting of vertices and links. The number of links attached to a vertex varies from 0 to 10.

The statistics is the following:

#of links #of vertices
0 497
1 361
2 226
3 134
4 65
5 35
6 15
7 6
8 2
10 1 (barna)
-----
1342

The champion is barna: 10 links

• barna: burna badna basna barda barja carna farna garna marna rarna

2 gismu have 8 links:

• manti: mapti masti manci manri canti danti ganti ranti
• panci: palci pandi panpi panzi canci lanci manci vanci

6 gismu have 7 links:

• brodi: bradi bredi bridi broda brode brodo brodu
• manci: matci manri manti canci lanci panci vanci
• marna: morna marxa barna carna farna garna rarna
• pinji: punji pilji pindi pinsi linji minji vinji
• ranti: ranji ranmi ranxi canti danti ganti manti
• salci: selci sakci satci kalci nalci palci ralci

15 gismu have 6 links:

• bargu: bangu bartu dargu kargu margu zargu
• canti: centi canci danti ganti manti ranti
• carna: cabna barna farna garna marna rarna
• cinla: cigla cirla civla cinba cinta cinza
• danlu: canlu daplu darlu dandu danfu dansu
• garna: gerna barna carna farna marna rarna
• gunta: gusta gunka gunma junta runta tunta
• kalci: kelci kalri nalci palci ralci salci
• karbi: korbi karli karni marbi parbi tarbi
• lanci: lanbi lanli canci manci panci vanci
• pinka: panka pilka ginka rinka pinca pinta
• sanji: kanji ranji sabji sarji sanli sanmi
• sanli: sakli sanji sanmi banli janli lanli
• santa: senta sanga fanta janta sakta salta
• tarbi: karbi marbi parbi tarci tarmi tarti

et cetera...

As a result, the totality of gismu will be split into groups (connected components) such that any two gismu within the same group can be connected by a continous line (that is one gismu can be obtained from another via a sequence of steps changing one letter at a time).

The statistics is the following:

size of group #of groups
1 497
2 90
3 29
4 14
5 5
6 4
7 1
8 1
9 4
11 1
26 1
33 1
60 1
131 1
161 1
--- -
1342 gismu 651 group

Curiously, on the map of the gismu space there are 2 huge continents (161 and 131 gismu), 3 smaller subcontinents (60, 33, 26) and an archipelago of smaller islands (sizes from 11 to 1 gismu).

Here is the list of the biggest cluster (161 gismu):

badri gadri bakri gacri bakni nakni balni nukni navni lacri vacri xalni bilni xadni balji balvi zalvi javni jadni jukni tagji xagji xagri tadji tamji fagri xanri fanri fatri tadni fadni lamji vamji fatci batci matci satci manri maxri dakli sakli sanli sakci ranmi sanmi sanji ranji ranti ranxi banfi banli janli lanli salci selci lanbi vanbi vanci lanci manci matli manti canci panci kandi pandi kanji pindi panpi panzi lindi linji linsi pinji pinsi palci bapli rapli racli marji sarji morji mavji marbi sirji sabji morsi porsi porpi karbi korbi karli karni parbi tarbi denci senci denmi sonci senpi kalci kelci kalri nelci nalci ralci jenmi penmi canti centi danti ganti mapni mapti masti carmi tarmi curmi carvi tarci tarti farvi cunmi xarci zarci dasni zasni datni zasti daski dasri damri ratni rutni catni basti decti kecti dacti mensi pensi menli penbi merli perli mirli pezli kinli minli minji dunli punli punji pilji pulji vinji kabri kagni kamni pulni pelji

and of the second biggest one (131 gismu):

cabna zabna carna cabra tabra cacra catra barna burna farna garna marna rarna barda karda barja basna lasna besna latna badna jemna remna jamna jerna gerna jirna jatna katna jalna morna marxa matra xatra ganra panra panka pinka pilka lanka xanka ginka rinka jalra jilra jisra jilka silka silna sipna sitna jinga jinsa rinsa tinsa xalka bebna lebna risna tisna tirna jivna nirna kajna kojna kalsa talsa kansa kanba nanba kanla nanca nanla mansa kensa cenba zenba cinba censa cinta pinta cilta pikta pinca cinla cinza vensa fenra kenra kunra jufra kufra lunra lunsa dunra civla livla livga cigla cirla bunda dunda dunja palta salta sakta santa janta junta fanta gunta runta tunta sanga sunga sudga senta sefta senva gunka tunka guska gunma tunba gasta gusta junla sunla surla fanva fanza

The gismu are given above in no particular order. The proper representaion would be a graphic one (vertices and links) but it needs a lot of handwork.

For any pair of gismu belonging to the same connected components we can introduce a distance as the minimal number of links connecting them. The maximal distance between two gismu turns out to be 27. There are only 4 chains of the length 27:

• cunmi-...-lacri
• cunmi-...-vacri
• farvi-...-lacri
• farvi-...-vacri

The 4 chains are basically variants of the same sequence starting with cunmi-curmi- or farvi-carvi, continuing as

carmi-tarmi-tarbi-marbi-marji-sarji-sanji-ranji-ranti-manti-manri-xanri-xagri-xagji-tagji-tadji-tadni-xadni-xalni-balni-bakri-badri-gadri-gacri-

and finishing with -lacri or -vacri.

When I have time, I'll put more details on my website --mi'e .evgenis.

doi .evgenis. .e'osai ko ranji skicu .i mi ba'e se cinri — mi'e nitcion.

there is unix graph making software (da vinci?) which can take a file of a network-ish description like you want to make, and produce graphical output. debian has used it for displaying the web of trust in the past. --jay

graphviz

sodipodi also works — mi'e tcravys.