Assortativity, Skewness, and Variation in New Orleans Facebook friendship subnetworks

For more information on the data or methods

This data is described well in Viswanath et al. (2009). (see Viswanath et al. 2009). All code is available from Alec McGail [am2873 at cornell dot edu], don't hesitate to reach out.

Helpers and data organization

Random subnetworks

The subnetworks are defined by randomly selecting an ego, and their friends, and the friends of their friends (3rd-order egonet). If this network is sizable enough, but not too sizable (100 < N < 2000) we calculate a whole bunch of network statistics from it and save these.

Friendship network

g.friends <- graph_from_data_frame(
  friendships[,c("f","t")],
  directed = F
)
g.friends <- simplify(g.friends)

There are 63731 individuals in the network, with a total of 817090 edges among them. Thus the average degree is 2*E/V = 25.6418384.

##               feld_predicts
## feld_predicts     -82.49703

There are 489 subnetworks total. For each subnetwork we have the following attributes:

assortativity, crit_deg_overall_theory, crit_deg_overall_true, crit_deg_para_theory, crit_deg_para_true, crit_p_overall_theory, crit_p_overall_true, crit_p_para_theory, crit_p_para_true, deg_meanfdeg_b, deg_meanfdeg_corr, mean_degree, mean_friends_degree, mean_maxfdeg, mean_meanfdeg, mean_medfdeg, median_degree, n_degAtLeastTwo, n_edges, n_nodes, p_deg_eq_median, p_deg_gt_mean, p_deg_gt_median, p_deg_lt_mean, p_deg_lt_median, p_fdeg_eq_median, p_fdeg_gt_mean, p_fdeg_gt_median, p_fdeg_lt_mean, p_fdeg_lt_median, p_meanfdeg_eq_mean, p_meanfdeg_eq_mydeg, p_meanfdeg_gt_mean, p_meanfdeg_gt_mydeg, p_meanfdeg_lt_mean, p_meanfdeg_lt_mydeg, p_medfdeg_eq_median, p_medfdeg_gt_mean, p_medfdeg_gt_median, p_medfdeg_lt_mean, p_medfdeg_lt_median, sd_degree, skew_degree, variance_degree, feld_predicts, var_mean, var_mean2, mean_med_Omean, mPvOm

ASV

Assortativity

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Skewness

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Variance

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Combinations

var_mean2 (rows) X var_mean2 (cols)

## Warning in data.frame(val = as.numeric(l), x = (0:(length(l) - 1))%%10, : NAs
## introduced by coercion

var_mean2 (rows) X mean_med_Omean (cols)

## Warning in data.frame(val = as.numeric(l), x = (0:(length(l) - 1))%%10, : NAs
## introduced by coercion

var_mean2 (rows) X deg_meanfdeg_corr (cols)

## Warning in data.frame(val = as.numeric(l), x = (0:(length(l) - 1))%%10, : NAs
## introduced by coercion

mean_med_Omean (rows) X var_mean2 (cols)

## Warning in data.frame(val = as.numeric(l), x = (0:(length(l) - 1))%%10, : NAs
## introduced by coercion

mean_med_Omean (rows) X mean_med_Omean (cols)

## Warning in data.frame(val = as.numeric(l), x = (0:(length(l) - 1))%%10, : NAs
## introduced by coercion

mean_med_Omean (rows) X deg_meanfdeg_corr (cols)

## Warning in data.frame(val = as.numeric(l), x = (0:(length(l) - 1))%%10, : NAs
## introduced by coercion

deg_meanfdeg_corr (rows) X var_mean2 (cols)

## Warning in data.frame(val = as.numeric(l), x = (0:(length(l) - 1))%%10, : NAs
## introduced by coercion

deg_meanfdeg_corr (rows) X mean_med_Omean (cols)

## Warning in data.frame(val = as.numeric(l), x = (0:(length(l) - 1))%%10, : NAs
## introduced by coercion

deg_meanfdeg_corr (rows) X deg_meanfdeg_corr (cols)

## Warning in data.frame(val = as.numeric(l), x = (0:(length(l) - 1))%%10, : NAs
## introduced by coercion

Does assortativity matter at all, given these other attributes?

m1 <- lm(p_meanfdeg_gt_mydeg ~ skew_degree + assortativity, data=nets.friends)
m2 <- lm(p_meanfdeg_gt_mydeg ~ skew_degree + var_mean2, data=nets.friends)
m3 <- lm(p_meanfdeg_gt_mydeg ~ assortativity + var_mean2, data=nets.friends)
m4 <- lm(p_meanfdeg_gt_mydeg ~ assortativity + var_mean2 + skew_degree, data=nets.friends)

top <- rbind(
  data.frame(y=m1$residuals, m=1+rnorm(length(m1$residuals))/10),
  data.frame(y=m2$residuals, m=2+rnorm(length(m1$residuals))/10),
  data.frame(y=m3$residuals, m=3+rnorm(length(m1$residuals))/10),
  data.frame(y=m4$residuals, m=4+rnorm(length(m1$residuals))/10)
)

ggplot(top) +
  geom_point(aes(x=m, y=y), size=1) +
  xlab("Model") +
  ylab("Residual")

Viswanath, Bimal, Alan Mislove, Meeyoung Cha, and Krishna P. Gummadi. 2009. “On the Evolution of User Interaction in Facebook.” In Proceedings of the 2Nd Acm Workshop on Online Social Networks, 37–42. WOSN ’09. New York, NY, USA: ACM. doi:10.1145/1592665.1592675.