Map equation centrality: community-aware centrality based on the map equation

Applied Network Science

Table 2 Details for eight empirical networks: their number of nodes, N, number of links, \(\left| E\right|\), average degree, k, epidemic threshold, \(p_\text {th}\); the number of communities inferred with Infomap, M, the effective number of communities \({\tilde{M}}\), and mixing, \(\mu\), both for link and node teleportation

Network	N	\(\left\| E\right\|\)	k	\(p_\text {th}\)	Link teleportation			Node teleportation
Network	N	\(\left\| E\right\|\)	k	\(p_\text {th}\)	M	\({\tilde{M}}\)	\(\mu\)	M	\({\tilde{M}}\)	\(\mu\)
Facebook friends	329	1954	11.9	0.048	21	13	0.129	22	13	0.115
Copenhagen	800	6429	16.1	0.038	37	29	0.499	36	29	0.499
Uni email*	1133	5452	19.2	0.027	50	32	0.406	55	34	0.409
Polblogs*	1222	19,024	31.1	0.010	88	6	0.164	51	6	0.177
Interactome yeast	1458	1993	2.7	0.161	166	142	0.237	178	154	0.247
Ego Facebook	4039	88,234	43.7	0.009	77	32	0.082	86	35	0.083
Power	4941	6594	2.7	0.348	428	377	0.163	465	416	0.177
Facebook organizations	5524	94,219	34.1	0.016	53	30	0.360	62	40	0.391
Physics collaborations	8798	27,416	6.2	0.066	610	491	0.218	656	537	0.227
Google*	15,763	171,206	21.7	0.001	597	260	0.470	600	225	0.518
PGP*	39,796	301,498	15.2	0.010	2851	1529	0.285	3285	1843	0.305
Facebook wall*	43,953	271,375	12.3	0.028	2995	1375	0.493	3228	1747	0.519