Example: Football (soccer) playersNetwork collected by Lothar Krempel describes the 22 soccer teams which participated in the World Championship in Paris, 1998. Players of the national team often have contracts in other countries. This constitutes a players market where national teams export players to other countries. Members of the 22 teams had contracts in altogether 35 countries. The 2-mode relation is arc(i, j) - player i has a contract in the country j.Counting which team exports how many players to which country can be described with a valued, asymmetric graph. The graph is highly asymmetric: some countries only export players, some countries are only importers. Hubs and authoritiesIn directed networks we can usually identify two types of important vertices: hubs and authorities. A vertex is a good hub, if it points to many good authorities, and it is a good authority, if it is pointed to by many good hubs. Hubs and authorities are related to eigenvector centrality. See:KLEINBERG, Jon M.: Authoritative Sources in a Hyperlinked Environment. Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms, edited by Howard Karloff (SIAM/ACM-SIGACT, 1998).Pictures Network AnalysisValued Inp Out Inp Out Deg Deg Hubs Authorities Deg Deg ---------------------------------------------------- ARG 2 2 0.2764013 0.0073580 4 13 AUT 3 5 0.1691211 0.0289530 3 11 BEL 2 4 0.0871006 0.0295895 3 8 BGR 0 4 0.1087431 0.0000000 0 10 BRA 2 5 0.2103657 0.0322629 12 12 CHE 2 0 0.0000000 0.0189380 2 0 CHL 0 3 0.0204822 0.0000000 0 3 CMR 0 9 0.1803360 0.0000000 0 20 COL 0 5 0.0496744 0.0000000 0 9 DEU 16 3 0.0713116 0.3097197 39 4 DNK 0 7 0.2454492 0.0000000 0 16 ESP 18 0 0.0000000 0.5789962 54 0 FRA 13 0 0.0000000 0.1634971 24 0 GBR 12 0 0.0000000 0.5355642 50 0 GRE 3 0 0.0000000 0.0635664 5 0 HRV 0 6 0.2602221 0.0000000 0 14 IRN 0 1 0.0403306 0.0000000 0 3 ITA 16 3 0.1038528 0.4502114 42 5 JAM 0 1 0.1627250 0.0000000 0 7 JPN 4 0 0.0000000 0.0637349 9 0 KOR 0 2 0.0181625 0.0000000 0 5 MAR 0 6 0.1746280 0.0000000 0 13 MEX 1 0 0.0000000 0.0027950 1 0 NGA 0 10 0.2098329 0.0000000 0 21 NLD 6 4 0.2711707 0.0799073 10 12 NOR 0 6 0.3800853 0.0000000 0 22 PRT 4 0 0.0000000 0.0522481 7 0 PRY 0 3 0.0643884 0.0000000 0 13 ROM 0 7 0.2620101 0.0000000 0 18 SCO 2 2 0.1698217 0.0814487 6 8 TUN 1 2 0.0481771 0.0075801 1 5 TUR 7 0 0.0000000 0.1587900 18 0 USA 3 3 0.0768484 0.0143101 4 5 YUG 0 6 0.4122957 0.0000000 0 21 ZAF 1 9 0.2264670 0.0091084 1 17
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