## 6 Experiments
### Datasets  
We use a variety of network datasets, of which the name, type and source are listed in the first three columns of Table 1. The set of graphs covers a broad range of network types, including citation networks, collaboration networks, communication networks, peer-to-peer networks, protein-protein interaction networks, router topology networks, social networks and webgraphs. We will only consider the largest connected component of each graph, which is always the vast majority of the original graph. We also mention that some directed graphs have been interpreted as if they were undirected, and that self-edges and parallel edges are ignored. These factors may cause minor differences between the number of nodes and edges that we present here, and the numbers presented in the source papers. In Table 1 we also present for each dataset the exact average eccentricity \(\overline{\varepsilon}(G)\), radius \(\Gamma(G)\), diameter \(\Delta(G)\) and center and periphery sizes \(|C(G)|\) and \(|D(G)|\). For a more detailed description of these graphs, we refer the reader to the source papers in which the datasets were introduced.  
Looking at the exact eccentricity distributions that we were able to compute, we can conclude that the distribution is not perfectly Gaussian as [32] suggests, but does appear to be unimodal. The distribution appears to be somewhat \"tailed\"; a positive skew is noticeable in Figure 1, which shows the relative eccentricity distribution of a number of graphs. The tail also becomes clear when comparing the average eccentricity value \(\overline{\varepsilon}(G)\) with the radius and diameter of the graph: for every dataset, the average eccentricity is closer to the radius. For example, for the cit-HepTh dataset with radius \(8\) and diameter \(15\), the average eccentricity is equal to \(10.14\).  
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline
**Dataset** & **Type** & **Source** & **Nodes** & **Edges** & \(\overline{\varepsilon}(\mathbf{G})\) & \(\overline{\Gamma}(\mathbf{G})\) & \(\Delta(\mathbf{G})\) & \(|C(G)|\) & \(|D(G)|\) \\ \hline yeast & protein & [24] & 1 846 & 4 406 & 13.28 & 11 & 19 & 48 & 4 \\ ca-HepTh & collab. & [25] & 8 638 & 49 612 & 12.53 & 10 & 18 & 74 & 4 \\ ca-HepPh & collab. & [25] & 11 204 & 235 238 & 9.40 & 7 & 13 & 12 & 17 \\ dip20090126 & protein & [26] & 19 928 & 82 406 & 22.01 & 15 & 30 & 1 & 2 \\ ca-CondMat & collab. & [13] & 21 363 & 182 572 & 10.58 & 8 & 15 & 6 & 11 \\ cit-HepTh & citation & [13] & 27 400 & 704 042 & 10.14 & 8 & 15 & 4 & 4 \\ Enron & commun. & [22] & 33 696 & 361 622 & 8.77 & 7 & 13 & 248 & 11 \\ cit-HepPh & citation & [13] & 34 401 & 841 568 & 9.18 & 7 & 14 & 1 & 2 \\ slashdot & commun. & [27] & 51 083 & 243 780 & 11.66 & 9 & 17 & 7 & 3 \\ p2p-Gnutella & peer-to-peer & [25] & 62 561 & 295 756 & 8.94 & 7 & 11 & 55 & 118 \\ facebook & social & [28] & 63 392 & 1 633 772 & 9.96 & 8 & 15 & 168 & 7 \\ epinions & social & [29] & 75 877 & 811 478 & 9.74 & 8 & 15 & 614 & 6 \\ soc-slash & social & [30] & 82 168 & 1 008 460 & 8.91 & 7 & 13 & 484 & 3 \\ itdk0304-klinks & router & [26] & 190 914 & 1 215 220 & 17.09 & 14 & 26 & 155 & 7 \\ web-Stanford & webgraph & [30] & 255 265 & 3 883 852 & 106.49 & 82 & 164 & 1 & 3 \\ web-Notredame & webgraph & [31] & 325 729 & 2 180 216 & 27.76 & 23 & 46 & 12 & 172 \\ dblp20080824 & collab. & [26] & 511 163 & 3 742 140 & 14.79 & 12 & 22 & 72 & 9 \\ eu-2005 & webgraph & [26] & 862 664 & 37 467 426 & 14.03 & 11 & 21 & 3 & 4 \\ flickr & social & [28] & 1 624 992 & 30 953 670 & 15.03 & 12 & 24 & 17 & 3 \\ as-Skitter & router & [13] & 1 694 616 & 22 188 418 & 21.22 & 16 & 31 & 5 & 2 \\ \hline \end{tabular}
\end{table}
Table 1: Number of nodes, edges, average eccentricity, radius, diameter, center size and periphery size of our datasets.