Hi,

I am a sport scientist using igraph (as R-package) heavily for one of my manuscripts. The reviewers of the manuscript want me to include mathematical equations for my calculated network metrics. I have managed to find equations for 7 out of the 9 metrics/functions. Unfortunately I am struggling with 2 of them, namely the functions `transitivity()`

and `edge_connectivity()`

. I was hoping someone would be willing to help me out.

I have read the igraph manual, tried to find the source code of the functions (to see the calculation, but what I can find in R it only refers to C functions) and read the literature that are in the references for the two specific functions. Unfortunately the references do not give an equation either.

For `transitivity()`

in the manual an equation is given for the special case of Barret (and weighted graphs).

weighted C_i = \frac{1}{s_i} \frac{1}{k_i-1} \sum_{j,h} \frac{w_{ij}+w_{ih}}{2 a_{ij} a_{ih} a_{jh}}

I use the default (type = â€śglobalâ€ť) and therefore was wondering if for me the transitivity is the same equations without the weight factor (W_{ij} + W_{ih} )/2?

Moreover in the description â€śsi is the strength of vertex i, see strength, aij are elements of the adjacency matrix, ki is the vertex degree, wij are the weights.â€ť

I was wondering what the vertex *degree* is?

For `edge_connectivity()`

I struggle more to find information how to â€śwrite it in a equationâ€ť. So far I am fairly certain it is an iteration instead of a equation, but Iâ€™m not sure how to write this out.

The piece in the manual states â€śThe edge connectivity of a graph is the minimum of the edge connectivity of every (ordered) pair of vertices in the graph. edge_connectivity calculates this quantity if neither the source nor the target arguments are given (ie. they are both NULL).â€ť

Does it start at a random edge, removes it and checks if the graph is connected?

Then also I have `checks = TRUE`

, the description is â€śWhether to check that the graph is connected and also the degree of the vertices.â€ť How does the function check if it is connected?

I would greatly appreciate if anyone would be willing to point me in the right direction. As a sport scientist it is quite a challenging task.