# Getting graph density on a graph with multiple edges

Hello everyone!

I am working on a swine movement network analysis. I am analyzing the inter-city movement of pigs in my country.

In the inter-city movement of pigs, I have 685 cities and 37138 shipments (name of network is Swine_Graph). Each city can have 1 or more pig shipment creating multiple edges in each node.

When I ran my graph density in R, I wrote the following:
graph.density(SwinePH_Graph)

It gave me a value of 0.079 (does this mean my graph density is 7.9%)

However, when I looked into the igraph R manual, I saw this statement in graph.density → “Note that this function may return strange results for graph with multiple edges, density is ill-defined for graphs with multiple edges”

If this is the case, how should I properly compute my graph density if I have multiple edges in one node?

It seems you are using a rather outdated version. Why don’t you use the latest? The statement in the documentation is much clearer:

• What do you mean when you say “graph density”? Can you explain the concept?
• Why are you trying to compute it?

While this may not sound like a response, in fact it is. I am trying to lead you onto the right path.

Hello szhorvat,

I would like to know the density of my network. I am working to compute the density of pig shipments. From my research in several articles, I saw that the formula for a directed network is

total number of edges/(total number of nodes*(total number of nodes - 1))

In my 1st network, my data seems to have a value of below 1:
37128/(685*684) = 0.079

However, in my second network where there are only few nodes (66 provinces), there seems to be a very big value:

31622/(66*65) = 7.37

My data involves animal shipments (edges) in different provinces (nodes). It is very possible that there are multiple shipments in one province. There was a suggestion to me to use the following formula:

D= total number of edges / (total number of nodes*(total number of nodes -1) * multiplicity factor

The multiplicity factor represents the number of shipments between the same pair of nodes.

Does this seem to be a logical way of computing for density given the nature of my network?