[igraph] average path length decreases between edge deleted graphs

[Benton, Paul]

Dear all,

I'm trying to understand what is happening between two different graphs. To do this I have started to look at some network statistics. The two graphs are identical except that one graph is a filtered graph, i.e. some edges have been deleted. The graphs are disconnected, undirected and unweighted. When I ask for the average path length I get 1.564 for the original network. For the filtered network I get 1.552. I know that the difference isn't much but I don't understand how the average can go down when I delete edges! How is this possible?

I have tried using some other software but they don't accept unconnected networks with average path length. 

The only thing I can think of is to look at each of the sub-graphs and find the average path length for those to check. However, I'm not sure how to automatically isolate sub-graphs. How can I do this?

Thank you for any help,

Cheers,

Paul

average.path.length(g)

[1] 1.564292

> average.path.length(g.alt)

[1] 1.551715

> g

IGRAPH UN-- 2321 8551 -- 

+ attr: id (v/n), name (v/c), label (v/c)

> g.alt

IGRAPH UN-- 2321 7973 -- 

+ attr: id (v/n), name (v/c), label (v/c)

> sessionInfo()

R version 2.15.1 (2012-06-22)

Platform: x86_64-apple-darwin9.8.0/x86_64 (64-bit)

locale:

[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:

[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:

[1] igraph_0.6-2