Last.fm songs

This bipartite network represent the user–song listening habits of last.fm users. Left nodes are users and right nodes are songs. An edge connects users and songs they have listened to.

Metadata

Code		`Ls`
Internal name		`lastfm_song`
Name		Last.fm songs
Data source		http://www.dtic.upf.edu/~ocelma/MusicRecommendationDataset/lastfm-1K.html
Availability		Dataset is available for download
Consistency check		Dataset passed all tests
Category		Interaction network
Node meaning		User, song
Edge meaning		Listening
Network format		Bipartite, undirected
Edge type		Unweighted, multiple edges
Temporal data		Edges are annotated with timestamps

Statistics

Size	n =	1,085,612
Left size	n₁ =	992
Right size	n₂ =	1,084,620
Volume	m =	19,150,868
Unique edge count	m̿ =	4,413,834
Wedge count	s =	22,053,978,162
Claw count	z =	139,516,276,582,416
Cross count	x =	1,074,730,261,041,871,232
Square count	q =	32,357,367,219
4-Tour count	T₄ =	347,084,940,232
Maximum degree	d_max =	183,103
Maximum left degree	d_1max =	183,103
Maximum right degree	d_2max =	17,601
Average degree	d =	35.281 2
Average left degree	d₁ =	19,305.3
Average right degree	d₂ =	17.656 8
Fill	p =	0.004 102 29
Average edge multiplicity	m̃ =	4.338 83
Size of LCC	N =	1,085,611
Diameter	δ =	6
50-Percentile effective diameter	δ_0.5 =	3.487 12
90-Percentile effective diameter	δ_0.9 =	3.897 45
Median distance	δ_M =	4
Mean distance	δ_m =	3.952 16
Gini coefficient	G =	0.908 531
Balanced inequality ratio	P =	0.111 067
Left balanced inequality ratio	P₁ =	0.289 593
Right balanced inequality ratio	P₂ =	0.161 995
Relative edge distribution entropy	H_er =	0.737 931
Power law exponent	γ =	2.713 84
Tail power law exponent	γ_t =	1.921 00
Degree assortativity	ρ =	−0.114 597
Degree assortativity p-value	p_ρ =	0.000 00
Spectral norm	α =	7,516.29
Algebraic connectivity	a =	0.518 714
Spectral separation	\|λ₁[A] / λ₂[A]\| =	1.043 10
Controllability	C =	1,083,628
Relative controllability	C_r =	0.998 172

Plots

Fruchterman–Reingold graph drawing

Degree distribution

Cumulative degree distribution

Lorenz curve

Spectral distribution of the adjacency matrix

Spectral distribution of the normalized adjacency matrix

Spectral distribution of the Laplacian

Spectral graph drawing based on the adjacency matrix

Spectral graph drawing based on the Laplacian

Spectral graph drawing based on the normalized adjacency matrix

Degree assortativity

Zipf plot

Hop distribution

Edge weight/multiplicity distribution

Temporal distribution

Diameter/density evolution

Inter-event distribution

Node-level inter-event distribution

Downloads

References

[1]	Jérôme Kunegis. KONECT – The Koblenz Network Collection. In Proc. Int. Conf. on World Wide Web Companion, pages 1343–1350, 2013. [ http ]
[2]	Òscar Celma. Music Recommendation and Discovery in the Long Tail. Springer, 2010.