Figure 1:
Sample ‘Hairball’ showing jazz players that performed with each other.
Figure 2:
Visone backbone layout of jazz player data set.
Figure 3:
Sample HB curve for jazz players that performed with each other.
Figure 4:
Neighbors plot for jazz players that performed with each other.
Figure 5:
Questions addressed by location of neighbor nodes.
Figure 6:
Sample directed neighbors plot for jazz player data set (Green = In, Red = Out).
Figure 7:
Force-directed representation of the Toaster data set.
Figure 8:
Backbone layout representation of the Toaster data set.
Figure 9:
HB representation of the Toaster data set (directionality ignored).
Figure 10:
HB representation of the inverse of neighbor nodes (e.g. gaps).
Figure 11:
HB inverse representation of just the top 100 ranked nodes with each other in Toaster data set.
Figure 12:
Force Atlas 2 on top 20 nodes in Toaster data set.
Figure 13:
HB chart of first 3,500 connections in Toaster data set.
Figure 15:
HB chart of third 3,500 connections in Toaster data set.
Figure 14:
HB chart of second 3,500 connections in Toaster data set.
Figure 16:
HB chart of suspended Iranian Twitter™ accounts, user-id replies, and no retweets.
Figure 17:
HB chart of suspended Iranian Twitter™ accounts, user-id replies, no retweets, first 200 nodes showing gaps among the top 3 and the next 40 nodes.
Figure 18:
Sample chart of CodeDNA™ cluster outputs of malware binaries.
Figure 19:
Sample CodeDNA™ cluster outputs of Linux coreutils binaries.
Figure 20:
Sample CodeDNA™ cluster output in standard hairball buster (blue = nodes, gray dots = links).
Figure 21:
Sample CodeDNA™ cluster output in HB with vertical offset.
Figure 22:
Sample CodeDNA™ cluster output in HB with vertical offset and highlighting nodes with highest similarity scores.
Table 1.
Performance calculations comparisons for HB vs backbone layout.
| Data sets | hb run time (s) | visone run time – quad Sim (s) | visone run time – tri Sim (s) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Filename | File size (B) | No. of nodes | No. of edges | 1 | 2 | 3 | Avg | 1 | 2 | 3 | Avg | 1 | 2 | 3 | Avg |
| random-1000-nodes.graphml | 341,365 | 1,000 | 5,002 | 0.25 | 0.25 | 0.25 | 0.25 | 2.0 | 1.7 | 1.6 | 1.8 | 1.5 | 1.1 | 1.3 | 1.3 |
| random-10000-nodes.graphml | 3,555,915 | 10,000 | 49,826 | 0.67 | 0.69 | 0.70 | 0.69 | 7.3 | 6.9 | 6.8 | 7.0 | 7.0 | 7.1 | 6.8 | 7.0 |
| random-100000-nodes.graphml | 37,271,224 | 100,000 | 500,061 | 10.01 | 11.74 | 6.55 | 9.43 | 139.4 | 120.1 | 118.5 | 126.0 | 129.0 | 119.7 | 119.1 | 122.6 |
| random-250000-nodes.graphml | 95,452,841 | 250,000 | 1,250,487 | 16.84 | 15.36 | 15.24 | 15.81 | 349.3 | 357.3 | 361.3 | 356.0 | 356.8 | 352.7 | 334.5 | 348.0 |
| random-500000-nodes.graphml | 193,263,339 | 500,000 | 2,501,346 | 26.21 | 25.71 | 24.47 | 25.46 | >1,200 | |||||||
| random-1000000-nodes.graphml | 388,461,043 | 1,000,000 | 4,997,089 | 44.25 | 43.75 | 45.19 | 44.40 | Visone could not load graphml file. Insufficient memory | |||||||
| code-dna.graphml | 155,222 | 28 | 292 | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | |||
| jazz-directed.graphml | 361,796 | 198 | 4,113 | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | <1 sec | |||
| toster_CA_Edge.graphml | 5,349,861 | 23,916 | 75,050 | 1.02 | 0.96 | 0.96 | 0.98 | 20.6 | 19.8 | 20.1 | 20.2 | 17.1 | 18.9 | 17.8 | 17.9 |
| iran-tweet-replies.no-retweet.by-userid.graphml | 294,153,484 | 228,626 | 440,244 | 1.26 | 1.12 | 1.13 | 1.17 | >1,200 | |||||||
Figure 23:
Displaying different measures of centrality in HB.
Table 2.
Comparing HB features to other graph analytic and visualization algorithms.
| Feature | Hairball buster | Histogram/node-degree display | Force-directed | Visone backbone | Adjacency matrix | Block modeling |
|---|---|---|---|---|---|---|
| Understanding node relationships and graph characteristics | ||||||
| 1. Distribution of nodes by degree | Yes | Yes | No | No | Nof | Nof |
| 2. Quickly determine the number of high-degree nodes | Yes | Yes | No | No | Yes | Nof |
| 3. Quickly identify which are the highest degree nodes | Yes | Yesa | Nob | No | Yes | Yes |
| 4. Determine if the highest degree nodes are directly connected to other high-degree nodes | Yes | No | Yesc | Nob | Yes | Yes |
| 5. Determine whether the highest degree nodes are connected to each other indirectly via two hops | Yes | No | Yes | Yesc | Yes | Yes |
| 6. Determine which lower-degree nodes are directly connected to the high-degree nodes | Yes | No | Yes | Yes | Yes | Yes |
| 7. Provide visual cue of how much difference exists between the degree of the nodes, especially high-degree nodes | Yes | Yes | No | No | No | Yes |
| 8. Determine if there is one central cluster or many clusters that contain the highest degree nodes | Yes | No | Yes | Yes | No | Yes |
| Representing large or directed networks, or with weighted links | ||||||
| 9. Provide log–log or semi–log representation for very large data sets | Yes | Yes | No | No | No | No |
| 10. Can visualize both directed and undirected graphs | Yes | No | Yese | Yese | Yes | Yes |
| 11. Determine which nodes connect to the highest weighted links | Yes | No | Yesd | Yes | Yesg | Yesg |
| Other centrality measures, standard format, low calculation cost | ||||||
| 12. Distribution of nodes by other centrality measures | Yes | Yes | No | No | No | No |
| 13. Provide a canonical representation of the graph | Yes | Yes | No | No | Yes | No |
| 14. Low calculation cost | Yes | Yes | No | No | Yes | Noh |
1 Notes: aIf displayed or available via tooltip display; bexcept for very small data sets; cfor small graphs or when edges are not occluded; din some cases; eif link weights displayed, e.g., by color or width; funless one can count number of node or links very carefully; gif link weights displayed as attributes of dots in the matrix; horder at least N 2 and most references state N 3.
Figure 24:
Comparing different types of graphs and algorithms.
Figure A1:
Sample Log10–log10 plot of jazz player data set with no offset.
Figure A2:
Sample offset of origin to 10,10 for Log10–log10 plot of jazz player data set.
Figure A3:
Sample offset of origin to 10,10 for semi–log plot of Toaster data set.