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
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
Graph data 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 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
Graph data 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
Graph data 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 **