Table 2.

Network characteristics of the research collaboration network at the University of Arkansas for Medical Sciences from 2006 to 2012.

G = (V,E)						The largest connected component: Gl = (Vl, El)
RCN	|V|	|E|	density (d)	average # of new edges	# of isolated components	|Vl|	|El|	clustering coefficients			characteristic path length (Lgl )		diversity (Dgl )
								Cgl	$C_{g_l}^{w^o}$	$C_{g_l}^{w^t}$	Lgl	$L_{g_l}^{w^r}$
2006	184	279	0.017	N/A	51	22	54	0.763	0.764	0.725	2.303	2.216	0.392
2007	275	678	0.018	+1.577	44	68	185	0.788	0.796	0.710	4.661	4.537	0.206
2008	276	532	0.014	−0.097	48	88	231	0.658	0.673	0.654	4.784	4.419	0.168
2009	262	590	0.017	+0.343	41	124	418	0.729	0.737	0.789	5.840	5.239	0.147
2010	292	1,412	0.033	+10.803	31	214	1,351	0.796	0.810	0.773	3.365	2.718	0.232
2011	310	1,083	0.023	−10.013	35	207	959	0.773	0.783	0.752	3.769	3.440	0.240
2012	282	1,084	0.027	+0.300	32	149	643	0.757	0.767	0.727	3.409	3.007	0.255
2006 – 2009	487	1,318	0.011	N/A	55	339	1,183	0.639	0.654	0.660	5.084	3.537	0.133
2010 – 2012	429	2,008	0.022	+16.271	38	348	1,959	0.747	0.761	0.700	3.560	1.961	0.173
2006 – 2012	652	2,867	0.014	N/A	57	523	2,787	0.645	0.664	0.608	3.735	1.967	0.168

^*G = (V,E) is the original network excluding the isolated individual nodes, while G_l is a subgraph of the largest connected component excluding not only the isolated individual nodes but also the smaller disconnected components (components that do not have a link to G_l). |V | and |E| are the number of nodes and the number of edges in the corresponding network, respectively. The density d, the average number of new edges, and the number of isolated components are calculated on the original graph. The clustering coefficient, the characteristic path length, and the diversity are calculated on G_l as these measures are not that meaningful in graphs with disconnected subgraphs. Note that for the clustering coefficient measure we have three different approaches: 1) the unweighted Watts and Strogatz definition $C_g^{ws}$, 2) the Barrat’s generalization to weighted graph ${(C_g^{ws})}^w$, and 3) the transitivity definition $C_g^t(\mathit{unweighted})$. For the characteristic path length we presented measures for both the weighted and unweighted models of the same network.