Center for Applied Internet Data Analysis
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

Average degreeNumber of nodes9,20417,44617,4177,485
Number of edges28,95940,80542,48456,949
Avg node degree6.294.684.8815.22
Degree distributionMax node degree2,0702,4982,6271,079
Exponent 2.252.152.17-
Power-law maximum degree1,4484,5464,331-
Joint degree distributionNormalized avg neighbor degree0.050.030.030.02
Normalized max neighbor degree0.050.040.040.03
Exponent of average neighbor degree1.491.451.45-
Assortative coefficient-0.24-0.19-0.19-0.04
ClusteringMean clustering0.460.290.330.49
Clustering coefficient0.030.020.020.31
Exponent0.330.340.34-
Rich club connectivityTop clique size16974
Exponent1.481.451.461.69
CorenessMin node coreness0000
Avg node coreness2.231.421.527.66
Max node coreness27272787
Core size475364128
Min degree in core68343199
Fringe size2,4565,0884,428442
Max degree in fringe5774
Exponent0.680.580.641.07
DistanceAvg distance3.123.693.653.54
Std deviation of distance0.650.880.860.80
Exponent0.070.070.070.09
EccentricityAverage eccentricity5.116.616.446.12
Graph Diameter71098
Min degree in center418841,079
Max degree in periphery1126
BetweennessAvg node betweenness11x10-57.6x10-57.5x10-517x10-5
Max node betweenness0.120.100.100.10
Exponent1.351.171.30-
Min edge betweenness11x10-93.2x10-93.2x10-917x10-9
Avg edge betweeness5.3x10-54.5x10-54.2x10-53.1x10-5
Max edge betweenness4.3x10-36.2x10-34.9x10-36.4x10-3
SpectrumLargest eigenvalue79.5373.0674.90150.86
Second largest eigenvalue-53.32-55.13-56.2668.63
Third largest eigenvalue36.4053.5455.3562.03
Fourth largest eigenvalue-36.21-40.91-42.0854.35

## 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 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 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 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 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 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

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

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

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

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 for skitter
Graph data skitter

Scatter plot for edge betweenness for BGP_tables
Graph data BGP_tables

Contour plot for edge betweenness for BGP_tables
Graph data BGP_tables

Scatter plot for edge betweenness for BGP_updates

Contour plot for edge betweenness for 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 **