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

Applied Network Science

Table 18 Summary of network characteristics

Networks	NetDep	Weak-Prominents (%)	Co-liaisonship Avg	Embed.	CC	Modular.	Non-zero TwDep neighbors	Overlap size	Good match
Collaboration astro-ph cond-mat cond-2005	High	High	High	High	High	High	High	Middle	\(\underset {\text {Louvain}}{\text {Low}}\)
Social artist facebook new sites	Low	Low*	Low*	Low	Low*	Middle*	Low	Low	\(\underset {\text {Louvain}}{\text {Middle}}\)
Communication Brightkite Email-Enron	Low	Low	Low	Low	Unclear	Middle	Middle	Middle	\(\underset {\text {Louvain}}{\text {High}}\)
Technological as-22july06 power	Highest	Low	Low	Unclear	Low	Unclear	Middle	Unclear	\(\underset {\text {Louvain}}{\text {Unclear}}\)
Biological ChCh-Miner PP-Decagon PP-Pathways Yeast	Low	Low	Unclear	Low	Low	Low	Lowest	High**	\(\underset {\text {Louvain}}{\text {Middle}}\)
Ground-truth com-amazon com-dblp	High	High	Middle	High	Unclear	High	High	Middle	\(\underset {\text {ground-truth}}{\text {Highest}}\)
LFR benchmark LFR _{20 500 2000} LFR _{7 60 4000}	Low	Low	Low	High	Middle	Middle	Low	Unclear	\(\underset {\text {ground-truth}}{\text {High}}\)

* except facebook, ** except Yeast
In the individual columns in the table, there are values of selected parameters of networks that we analyzed. Each value of individual parameters comes from the experiments performed; if ‘unclear’ is listed, the networks are different in this parameter; the value of ‘Non-zero TwIndep neighbors’ represents the proportion of nodes that have at least one neighbor with which they are mutually dependent; ‘Overlap size ’ is estimated based on both maximum and average values.
There is a similarity between collaboration and ground-truth networks; however, this is expected because the com-dblp network is also one of the collaboration networks. Social, communication, and biological networks show further similarity; communication networks are distinguished by a high match of zones with non-overlapping communities, and, on the other hand, large overlaps exist in biological networks. Technological networks and LFR benchmark networks differ from these three network groups; technological networks have a high value of NetDep, the total network dependency; the LFR benchmark networks differ in having high embeddedness value. Anobii and com-youtube networks are not listed because they were not the subject of all experiments