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
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

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


PDF of node degree distribution

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


Joint degree distribution



CCDF of average neighbor connectivity

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


Average neighbor connectivity as a function of node degree

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 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 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 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 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 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 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 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 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

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


Local clustering as a function of node degree

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

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 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

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


Coreness



CCDF of node coreness

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


Node coreness as a function of node degree

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


Distance



PDF of distance distribution

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


Average distance as a function of node degree

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


Eccentricity



PDF of eccentricity

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


Eccentricity as a function of node degree

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


Betweenness



CCDF of node bwtweenness

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


Betweenness as a function of node degree

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


CCDF of edge betweenness

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


Scatter plot for edge betweenness for skitter

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

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

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

Scatter plot for edge betweenness for WHOIS
Graph data WHOIS

Contour plot for edge betweenness for WHOIS

Contour plot for edge betweenness for WHOIS
Graph data WHOIS

Spectrum



CCDF of graph spectrum

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

Related Objects

See https://catalog.caida.org/details/paper/2005_tr_2005_02/ to explore related objects to this document in the CAIDA Resource Catalog.