2 added 571 characters in body
source | link

Both of these hypotheses relate to assortativity. Assortativity is a correlation metric that indicates whether nodes are likely to be connected to similar others (positive assortativity) or dissimilar others (negative assortativity).

Note that for your question about "popularity" you need to make a decision about how to measure popularity. The most straightforward metric would be the sum of incoming friendship weights. However, you have a few choices here -- check out the idea of network centrality.

IfNote that this does not directly provide for hypothesis testing in the statistical sense. Networks are difficult in this sense, because you wantgenerally only have a single network, so your statistical sample size is N=1. One common approach to trydeveloping a hypothesis test is to combine those two scoresgenerate many random network with the same average degree as your empirical networks (see whichand the same set of node attributes) and generate a null hypothesis distribution of the metric of interest, in this case assortativity. (That is more important, you generate many assortativity scores from your data, get the standard deviation, and determine a z-score for predicting friendshipyour empirical data point.) you could

For more advanced techniques, look into Exponential Random Graph Modeling (ERGM) which uses techniquesis comparable to linearmultivariate regression toand can test any set of potential tie predictors in addition to homophily.

Both of these hypotheses relate to assortativity. Assortativity is a correlation metric that indicates whether nodes are likely to be connected to similar others (positive assortativity) or dissimilar others (negative assortativity).

Note that for your question about "popularity" you need to make a decision about how to measure popularity. The most straightforward metric would be the sum of incoming friendship weights. However, you have a few choices here -- check out the idea of network centrality.

If you want to try to combine those two scores (see which is more important for predicting friendship) you could look into Exponential Random Graph Modeling (ERGM) which uses techniques comparable to linear regression to test any set of potential tie predictors in addition to homophily.

Both of these hypotheses relate to assortativity. Assortativity is a correlation metric that indicates whether nodes are likely to be connected to similar others (positive assortativity) or dissimilar others (negative assortativity).

Note that for your question about "popularity" you need to make a decision about how to measure popularity. The most straightforward metric would be the sum of incoming friendship weights. However, you have a few choices here -- check out the idea of network centrality.

Note that this does not directly provide for hypothesis testing in the statistical sense. Networks are difficult in this sense, because you generally only have a single network, so your statistical sample size is N=1. One common approach to developing a hypothesis test is to generate many random network with the same average degree as your empirical networks (and the same set of node attributes) and generate a null hypothesis distribution of the metric of interest, in this case assortativity. (That is, you generate many assortativity scores from your data, get the standard deviation, and determine a z-score for your empirical data point.)

For more advanced techniques, look into Exponential Random Graph Modeling (ERGM) which uses is comparable to multivariate regression and can test any set of potential tie predictors in addition to homophily.

1
source | link

Both of these hypotheses relate to assortativity. Assortativity is a correlation metric that indicates whether nodes are likely to be connected to similar others (positive assortativity) or dissimilar others (negative assortativity).

Note that for your question about "popularity" you need to make a decision about how to measure popularity. The most straightforward metric would be the sum of incoming friendship weights. However, you have a few choices here -- check out the idea of network centrality.

If you want to try to combine those two scores (see which is more important for predicting friendship) you could look into Exponential Random Graph Modeling (ERGM) which uses techniques comparable to linear regression to test any set of potential tie predictors in addition to homophily.