Spectral separation

These are the values of the spectral separation (|λ1[A] / λ2[A]|) for all networks to which the statistic applies and for which it was computed. In total, it has been computed for 158 networks.

The spectral separation (|λ1[A] / λ2[A]|) equals the largest absolute eigenvalue of the adjacency matrix divided by the second largest absolute eigenvalue. The value is at least one. Larger values indicate "less diversity" in the network structure, in the sense that the adjacency matrix approaches a rank-one matrix. Low values (just slightly larger than one) indicate many independent substructures in the network; this can be interpreted as "more diversity", "more structure", or "more complexity".

The full definition of the spectral separation as well as its properties and relationships to other graph statistics can be found in the KONECT handbook.

NameAttributes1[A] / λ2[A]|
South African companies
1.658 85
Southern women (small)
1.574 97
HIV
1.000 32
Zachary karate club
1.351 34
Highland tribes
1.332 48
Taro exchange
1.261 79
Southern women (large)
1.539 21
Zebra
3.514 66
Corporate club memberships
1.806 22
Corporate leaderships
1.755 08
Kangaroos
2.307 23
Iceland
1.480 28
Wikiquote edits (kr)
1.171 57
Contiguous USA
1.166 23
Rhesus macaques
1.923 12
Dolphins
1.211 80
Chesapeake Bay
1.599 44
American Revolution
1.103 10
Wikibooks edits (gn)
1.289 94
Wikibooks edits (rm)
1.247 02
Wikiquote edits (ang)
1.729 53
Wikiquote edits (ks)
1.022 65
Wikibooks edits (bm)
1.252 32
Wikiquote edits (bm)
1.163 31
Crisis in a Cloister
1.052 39
Wikibooks edits (bi)
1.169 49
Cattle
2.240 31
PDZBase
1.000 15
Wiktionary edits (rn)
1.013 15
Wiktionary edits (mh)
2.145 14
Wikiquote edits (tk)
1.438 46
Wiktionary edits (ch)
1.153 64
Train bombing
2.162 47
Wikiquote edits (ug)
1.537 08
Wiktionary edits (av)
1.099 17
Sheep
2.772 90
Wiktionary edits (ak)
1.137 72
Gene fusion
1.000 84
Wikibooks edits (ks)
1.008 70
Les Misérables
1.333 38
Wikibooks edits (ch)
1.236 42
Wikibooks edits (as)
2.313 53
Wikibooks edits (my)
1.879 80
Wikibooks edits (aa)
1.671 14
Wikibooks edits (nah)
1.170 92
Bison
2.736 85
Wikibooks edits (got)
1.241 79
Wiktionary edits (cr)
2.461 09
Wikiquote edits (als)
1.498 15
Similarities (DBpedia)
2.244 37
Euroroads
1.023 07
Facebook (NIPS)
1.010 22
Caenorhabditis elegans
1.432 48
U. Rovira i Virgili
1.223 03
Florida ecosystem wet
1.204 30
Florida ecosystem dry
1.104 37
US power grid
1.132 21
Route views
1.214 21
Prosper groups
1.582 95
OpenFlights (Opsahl)
1.483 18
US airports
2.701 67
Twitter lists
1.271 08
Infectious
1.081 97
Prosper listings
1.150 51
Hypertext 2009
1.006 03
Haggle
5.811 49
Google+ (NIPS)
1.210 22
CAIDA
1.235 74
arXiv cond-mat
1.027 69
UC Irvine forum
1.583 30
Filmtipset friendships
1.067 36
Marvel
1.290 64
Cora
1.025 23
Sexual escorts
1.088 40
JUNG/Javax
1.044 74
UC Irvine messages
1.149 58
Java Development Kit
1.032 18
Gnutella (31)
1.137 32
Manufacturing emails
1.122 82
Writers
1.220 40
Condensed matter (2005)
1.327 44
MovieLens 100k
1.120 21
arXiv astro-ph
1.250 87
Digg
1.142 43
MovieLens tag–item
1.226 55
MovieLens user–item
1.279 70
MovieLens user–tag
1.023 22
Brightkite
1.305 74
Producers
1.075 50
Record labels
1.169 19
Occupations
1.250 24
Slashdot
1.229 25
YouTube
1.235 41
Actors (DBpedia)
1.349 30
DBpedia locations
1.989 43
arXiv hep-th
1.223 53
Edinburgh Associative Thesaurus
1.526 69
Internet topology
2.341 89
arXiv hep-ph
1.049 45
EU institution
1.602 95
Github
2.027 71
Genres (DBpedia)
1.217 52
DBpedia countries
1.281 18
Slashdot Zoo
1.065 43
SAP forums
1.208 29
WordNet
1.026 21
Wikibooks edits (fr)
2.773 25
WikiSigned
1.010 66
Gowalla
1.395 92
Twitter (ICWSM)
1.050 05
Reuters-21578
1.592 83
Facebook (WOSN)
1.243 97
Wikinews edits (fr)
6.746 75
Teams
1.267 49
Epinions
1.270 22
Notre Dame
1.000 00
MovieLens 1M
1.362 99
Reality Mining
1.950 75
Facebook
1.011 73
CiteSeer
1.082 53
vi.sualize.us user–tag
2.145 22
Flickr
1.197 14
Enron
1.702 73
vi.sualize.us tag–item
3.644 49
vi.sualize.us user–item
2.101 98
Stanford
1.051 30
Wikiquote edits (en)
1.101 48
Filmtipset comments
2.351 83
Discogs label–genre
2.985 07
arXiv hep-th
1.535 15
Wikipedia dynamic (simple)
1.342 24
Amazon (TWEB, 0601)
1.089 28
Wikipedia words (en)
2.922 42
Wikipedia categories (en)
1.095 29
Discogs label–style
2.116 92
Wikibooks edits (en)
1.109 68
BibSonomy user–tag
1.105 36
BibSonomy user–item
1.621 94
BibSonomy tag–item
1.651 31
Twitter tag–item
2.926 07
CiteULike user–tag
1.037 44
CiteULike tag–item
1.430 65
CiteULike user–item
1.448 50
WebUni Magdeburg
1.047 85
arXiv hep-ph
1.120 47
Wikinews edits (en)
1.267 40
Wikipedia conflict
2.185 17
Wiktionary edits (de)
1.281 32
Amazon ratings
3.442 97
Discogs artist–genre
4.534 39
Discogs
1.955 97
DBpedia
1.003 51
Catster/Dogster
1.372 33
Discogs artist–style
4.222 26
Libimseti.cz
1.048 45
Wikipedia dynamic (nl)
1.350 50
Google+ (IMC12)
1.316 52
Wikipedia dynamic (pl)
1.554 97