Ego-zones: non-symmetric dependencies reveal network groups with large and dense overlaps

Applied Network Science

Table 16 Match of zones and communities detected by Louvain algorithm

Network	Comm.	Comm. size		Zone size		MCC		Modularity	Comm.	Zone
		Max	Avg	Max	Avg	Max	Avg		embed.	embed.
anobii	882	37944	177.971	1084	9.672	1.000	0.879	0.573	0.797	0.651
artist	30	10139	1683.833	73	22.033	1.000	0.479	0.604	0.776	0.328
as-22july06	42	5099	546.738	1991	187.690	1.000	0.512	0.663	0.787	0.222
astro-ph	55	648	269.909	382	65.291	0.974	0.423	0.755	0.695	0.640
Brightkite	457	12119	124.155	375	9.626	1.000	0.856	0.660	0.913	0.828
com-amazon	252	11727	1328.821	451	39.222	1.000	0.354	0.926	0.965	0.755
com-dblp	463	33896	684.838	255	27.633	1.000	0.716	0.810	0.910	0.772
com-youtube	9264	197482	122.476	10538	12.265	1.000	0.904	0.686	0.843	0.641
cond-mat	82	759	169.037	75	27.098	1.000	0.413	0.862	0.835	0.704
cond-mat-2005	79	3266	461.494	271	56.190	0.931	0.366	0.786	0.980	0.966
Email-Enron	308	7550	109.403	1371	27.461	1.000	0.891	0.584	0.968	0.902
facebook	16	548	252.438	1017	257.312	1.000	0.727	0.835	0.946	0.644
ChCh-Miner	8	397	188.750	78	31.875	0.636	0.376	0.392	0.616	0.359
new_sites	65	4964	429.492	177	23.738	1.000	0.550	0.611	0.802	0.640
power	40	233	123.525	24	13.675	0.561	0.339	0.935	0.963	0.723
PP-Decagon	20	5649	953.250	614	56.650	1.000	0.550	0.445	0.710	0.568
PP-Pathways	17	4626	1265.941	652	97.941	1.000	0.475	0.386	0.715	0.446
Yeast	24	258	92.667	32	15.417	1.000	0.482	0.587	0.845	0.729
LFR _{20 500 2000}	48	1161	208.333	88	41.208	1.000	0.586	0.659	0.764	0.587
LFR _{7 60 4000}	45	456	222.000	67	37.222	0.534	0.338	0.578	0.614	0.387

The table shows very high agreement between communities and zones for the communications networks (Email-Enron, Brightkite, anobii) and the video-sharing network (com-youtube), and high agreement for the facebook and com-dblp networks. In these networks, the zones correspond well to the communities. This means that in these networks, communities, similarly to zones, form around egos – those nodes on which the nodes in their surroundings are directly or indirectly dependent. However, it should be noted that many other zones were detected in these networks, predominantly nested in the communities and their corresponding zones