Dear Yae Ji Kim ,

Look the link, maybe useful.

https://www.nature.com/articles/s41598-018-29927-0

Regards,

Shafagat

Dear Yaeji Kim,

even if all the graph theoretical descriptos impinge on the same raw material (a set of nodes linked by edges) their actual empirical correlation depends upon the specific wiring structures of the considered network. Thus the dependency of chracteristic length from average degree is much weaker in protein contact networks than in Erdos Renyi theoretical constructs of metabolic networks, This implies that we can make use of the correlation pattern among graph descriptors (see attached file) to discriminate different network architectures. If you look to loading matrix of the components (factors) describing the data set made by different kind of both real and theoretical networks you will discover many components in which the different graph descriptors enter with a very variable loading profile so pointing to a rich and variegates structure. If, on the contrary, the correlation among graph descriptors were only based upon algebraic reasons, this should not be possible and the extracted factors had not any heuristic power in discriminating different network types.

While I am not familiar with your field of study, I could probably give some explanation about the graph metrics.

--Global Efficiency (GE) values increase as connectivity increases (i.e., vertices are connected with less edges)

--On the contrary, Char Path Length (CPL) values decrease as connectivity increases (less number of edges required to connect)

--Mean clustering coefficient (MCC) is another measure that increases as connectivity increases.

This explains why MCC is postitively correlated with GE and negatively correlated with CPL.

In essence, as the number of network edges increases:

1) Vertices are likely to be connected with shorter paths, thus higher GE and lower CPL

2) Vertices have a higher chance to have high clustering coefficient values, thus the network has higher MCC

Despite being correlated, they show different things. For example, GE shows how "close" the network vertices are, while MCC shows to what extend the connections of a vertice are also connected.

I would aslo note that the exact value of correlation depends on the network. You might find medium correlations (~0.5) or rather strong (~0.8). Depends on the data and the way the edges are connected!

Hope that it helps!