[igraph] How to test if there is any relationship between attributes of edges and nodes

[capitano . nemo]

Hello list,

I want to test whether two attributes of each pair of nodes in my graph 
have any relationship with one attribute of the edge linking them.

I have some problem both on the statistical and coding side in getting 
to that.

Let's take this graph randomly generated (only for purpose of 
reproducibility):

  library(igraph)

  # Create random graph
  vertices <- 100
  g <- random.graph.game(vertices, .05, directed=FALSE)

  # Assign attribute 1 to vertices
  V(g)$size <- sample(1:100, vertices, replace=T)

  # Assign attribute 2 to vertices
  V(g)$time <- sample(1000:2000, vertices, replace=T)

  # Assign weight to edges
  edges <- ecount(g)
  E(g)$weight <- sample(1:10, edges, replace=T)

Each node represents an event with V(g)$size indicating the number of 
participants and V(g)$time the time of the event. E(g)$weight indicates 
the number of participants shared by the two nodes connected by the 
edge; no edge can be understood as E(g)$weight = 0.

I want to test two hypothesis:
1) When V(g)$size increases for one or both nodes, E(g)$weight of the 
connecting edge also increases;
2) When the difference between the two V(g)$time decreases (thus the 
event happens closer in time), E(g)$weight of the connecting edge 
increases.

I think I could attempt to use a regression analysis for the second 
hypothesis using the difference in time as the independent variable and 
E(g)$weight as the dependent variable. But what to do (statistically) 
and how to do it (in terms of code) with the first hypothesis? I have 
some conceptual problem here since the independent variable is split 
into two different nodes and assumes two different values... Also 
wouldn't be better to test both independent variables V(g)$size and 
difference in V(g)$time in the same model?