Comparative Analysis of the Internet AS-Level Topologies: Master Comparison

We calculate the most commonly used statistical characteristics of skitter, BGP and WHOIS topologies. Detailed explanations of the topologies and metric definitions are available in "Lessons from Three Views of Internet AS-Level Topology".

Master Comparison Table

Group	Metrics	skitter	BGP_tables	BGP_updates	WHOIS
Average degree	Number of nodes	9,204	17,446	17,417	7,485
	Number of edges	28,959	40,805	42,484	56,949
	Avg node degree	6.29	4.68	4.88	15.22
Degree distribution	Max node degree	2,070	2,498	2,627	1,079
	Exponent	2.25	2.15	2.17	-
	Power-law maximum degree	1,448	4,546	4,331	-
Joint degree distribution	Normalized avg neighbor degree	0.05	0.03	0.03	0.02
	Normalized max neighbor degree	0.05	0.04	0.04	0.03
	Exponent of average neighbor degree	1.49	1.45	1.45	-
	Assortative coefficient	-0.24	-0.19	-0.19	-0.04
Clustering	Mean clustering	0.46	0.29	0.33	0.49
	Clustering coefficient	0.03	0.02	0.02	0.31
	Exponent	0.33	0.34	0.34	-
Rich club connectivity	Top clique size	16	9	7	4
Rich club connectivity	Exponent	1.48	1.45	1.46	1.69
Coreness	Min node coreness	0	0	0	0
	Avg node coreness	2.23	1.42	1.52	7.66
	Max node coreness	27	27	27	87
	Core size	47	53	64	128
	Min degree in core	68	34	31	99
	Fringe size	2,456	5,088	4,428	442
	Max degree in fringe	5	7	7	4
	Exponent	0.68	0.58	0.64	1.07
Distance	Avg distance	3.12	3.69	3.65	3.54
	Std deviation of distance	0.65	0.88	0.86	0.80
	Exponent	0.07	0.07	0.07	0.09
Eccentricity	Average eccentricity	5.11	6.61	6.44	6.12
	Graph Radius	4	5	5	4
	Graph Diameter	7	10	9	8
	Min degree in center	4	188	4	1,079
	Max degree in periphery	1	1	2	6
Betweenness	Avg node betweenness	11x10^-5	7.6x10^-5	7.5x10^-5	17x10^-5
	Max node betweenness	0.12	0.10	0.10	0.10
	Exponent	1.35	1.17	1.30	-
	Min edge betweenness	11x10^-9	3.2x10^-9	3.2x10^-9	17x10^-9
	Avg edge betweeness	5.3x10^-5	4.5x10^-5	4.2x10^-5	3.1x10^-5
	Max edge betweenness	4.3x10^-3	6.2x10^-3	4.9x10^-3	6.4x10^-3
Spectrum	Largest eigenvalue	79.53	73.06	74.90	150.86
	Second largest eigenvalue	-53.32	-55.13	-56.26	68.63
	Third largest eigenvalue	36.40	53.54	55.35	62.03
	Fourth largest eigenvalue	-36.21	-40.91	-42.08	54.35

Degree distribution

CCDF of node degree distribution
Graph data skitter ** BGP tables ** BGP updates ** WHOIS **

PDF of node degree distribution
Graph data skitter ** BGP tables ** BGP updates ** WHOIS **

Joint degree distribution

CCDF of average neighbor connectivity
Graph data skitter ** BGP tables ** BGP updates ** WHOIS **

Average neighbor connectivity as a function of node degree
Graph data skitter ** BGP tables ** BGP updates ** WHOIS **

Scatter plot for degree-degree distribution P(k1,k2) for skitter

Scatter plot for degree-degree distribution P(k1,k2) for skitter

Scatter plot of the ratio of the joint degree distribution of skitter to the joint degree distribution of 1K-random (PK) graph having skitter's degree distribution
Graph data skitter

Contour plot for degree-degree distribution P(k1,k2) for skitter

Contour plot for degree-degree distribution P(k1,k2) for skitter

Contour plots of the ratio of the joint degree distribution of skitter to the joint degree distribution of 1K-random graph (PK) having skitter's degree distribution
Graph data skitter

Scatter plot for degree-degree distribution P(k1,k2) for BGP_tables

Scatter plot for degree-degree distribution P(k1,k2) for BGP_tables

Scatter plot of the ratio of the joint degree distribution of BGP_tables to the joint degree distribution of 1K-random graph (PK) having BGP_tables' degree distribution
Graph data BGP_tables

Contour plot for degree-degree distribution P(k1,k2) for BGP_tables

Contour plot for degree-degree distribution P(k1,k2) for BGP_tables

Contour plot of the ratio of the joint degree distribution of BGP_tables to the joint degree distribution of 1K-random graph (PK) having BGP_tables' degree distribution
Graph data BGP_tables

Scatter plot for degree-degree distribution P(k1,k2) for BGP_updates

Scatter plot for degree-degree distribution P(k1,k2) for BGP_updates

Scatter plot of the ratio of the joint degree distribution of BGP_updates to the joint degree distribution of 1K-random graph (PK) having BGP_updates' degree distribution
Graph data BGP_updates

Contour plot for degree-degree distribution P(k1,k2) for BGP_updates

Contour plot for degree-degree distribution P(k1,k2) for BGP_updates

Contour plot of the ratio of the joint degree distribution of BGP_updates to the joint degree distribution of 1K-random graph (PK) having BGP_updates' degree distribution
Graph data BGP_updates

Scatter plots for degree-degree distribution P(k1,k2) for WHOIS

Scatter plots for degree-degree distribution P(k1,k2) for WHOIS

Scatter plot of the ratio of the joint degree distribution of WHOIS to the joint degree distribution of 1K-random graph (PK) having WHOIS's degree distribution
Graph data WHOIS

Contour plot for degree-degree distribution P(k1,k2) for WHOIS

Contour plot for degree-degree distribution P(k1,k2) for WHOIS

Contour plot of the ratio of the joint degree distribution of WHOIS to the joint degree distribution of 1K-random graph (PK) having WHOIS' degree distribution
Graph data WHOIS

Clustering

CCDF of local clustering
Graph data skitter ** BGP tables ** BGP_updates ** WHOIS **

Local clustering as a function of node degree
Graph data skitter ** BGP tables ** BGP_updates ** WHOIS **

Clustering comparison with 2K, 1K and 0K-graphs for skitter
Graph data skitter

Clustering comparison with PKK, PK and K-graphs for BGP_tables

Clustering comparison with 2K, 1K and 0K-graphs for BGP_tables
Graph data BGP tables

Clustering comparison with PKK, PK and K-graphs for BGP_updates

Clustering comparison with PKK, PK and K-graphs for BGP_updates

Clustering comparison with 2K, 1K and 0K-graphs for BGP_updates
Graph data BGP_updates

Clustering comparison with PKK, PK and K-graphs for WHOIS

Clustering comparison with 2K, 1K and 0K-graphs for WHOIS
Graph data WHOIS

Rich club connectivity

CCDF of rich club connectivity
Graph data skitter ** BGP tables ** BGP_updates ** WHOIS **

Coreness

CCDF of node coreness
Graph data skitter ** BGP tables ** BGP_updates ** WHOIS **

Node coreness as a function of node degree
Graph data skitter ** BGP tables ** BGP_updates ** WHOIS **

Distance

PDF of distance distribution
Graph data skitter ** BGP tables ** BGP_updates ** WHOIS **

Average distance as a function of node degree
Graph data skitter ** BGP tables ** BGP_updates ** WHOIS **

Eccentricity

PDF of eccentricity
Graph data skitter ** BGP tables ** BGP updates ** WHOIS

Eccentricity as a function of node degree
Graph data skitter ** BGP tables ** BGP updates ** WHOIS

Betweenness

CCDF of node bwtweenness
Graph data WHOIS ** BGP updates ** skitter ** BGP tables **

Betweenness as a function of node degree
Graph data WHOIS ** BGP updates ** skitter ** BGP tables **

CCDF of edge betweenness
Graph data WHOIS ** BGP updates ** skitter ** BGP tables **

Scatter plot for edge betweenness for skitter
Graph data skitter

Contour plot for edge betweenness B(k1,k2) for skitter

Contour plot for edge betweenness for skitter
Graph data skitter

Scatter plot for edge betweenness for BGP_tables
Graph data BGP_tables

Contour plot for edge betweenness B(k1,k2) for BGP_tables

Contour plot for edge betweenness for BGP_tables
Graph data BGP_tables

Scatter plot for edge betweenness for BGP_updates
Graph data BGP_updates

Contour plot for edge betweenness B(k1,k2) for BGP_updates

Contour plot for edge betweenness for BGP_updates
Graph data BGP_updates

Scatter plot for edge betweenness for WHOIS
Graph data WHOIS

Contour plot for edge betweenness for WHOIS
Graph data WHOIS

Spectrum

Absolute values of top 10% of eigenvalues ordered by their normalized rank.
Graph data skitter ** BGP tables ** BGP updates ** WHOIS **