Design Considerations for a Social Network-Based Recommendation System (SNRS) - Community-Built Databases: Research and Development - page 78

Since homophily is the main assumption for building SNRS, we would like to
see whether homophily appears in the Yelp dataset. In the following studies, we
focus on two questions: (1) whether friends tend to review the same restaurant than
non-friends and (2) whether friends tend to give similar ratings to those of non-
friends.

4.3.1 Review Correlations of Immediate Friends

In this study, we want to know if a user reviews a restaurant, what is the chance that
at least one of the user's immediate friends has also reviewed the same restaurant?
To answer this question, we count, for each user, the percentage of restaurants
that have also been reviewed by at least one immediate friend. The average
percentage over all users in the dataset is 18.6%. As a comparison, we calculate
the same probability by assuming immediate friends review restaurants uniformly
at random and independently. In a social network with n users, for a user with q
immediate friends and a restaurant with m reviewers (including the current user),
the chance that at least one of q immediate friends appears in m reviewers is

n q n

1 1

1 . We calculate this value for every user and every

m m

1 1

restaurant the user reviewed. The average probability over all users is only 3.7%.
Compared with the 18.6% observed in the dataset, it is clear that immediate friends
do not review restaurants randomly.
We also compare the average number of co-reviewed restaurants between any
two immediate friends and any two random users on Yelp. The results are 0.85 and
0.03, respectively, which again illustrates the tendency for immediate friends to co-
review the same restaurants.

4.3.2 Rating Correlations of Immediate Friends

To validate whether immediate friends tend to give ratings that are more similar
than those of non-friends, we compare the average rating differences (in absolute
values) for the same restaurant between reviewers who are immediate friends, and
non-friends. We find that for every restaurant in our dataset, if two reviewers are
immediate friends, their ratings of this restaurant differ by 0.88 on average with a
deviation of 0.89. If they are not, their rating difference is 1.05 and the standard
deviation is 0.98. This result clearly demonstrates that immediate friends, on
average, give more similar ratings than do non-friends.
From the studies above, we can see that immediate friends at Yelp have stronger
correlations than non-friends when reviewing the same restaurants and give similar
ratings. In other words, homophily indeed exists when friends rate items. This
observation further leads us to the design of SNRS in Sect. 4.4 .