  In social networks, it is conventionally thought that two individuals with
more overlapped friends tend to establish a new friendship, which could be
stated as homophily breeding new connections. While the recent hypothesis of
maximum information entropy is presented as the possible origin of effective
navigation in small-world networks. We find there exists a competition between
information entropy maximization and homophily in local structure through both
theoretical and experimental analysis. This competition means that a newly
built relationship between two individuals with more common friends would lead
to less information entropy gain for them. We conjecture that in the evolution
of the social network, both of the two assumptions coexist. The rule of maximum
information entropy produces weak ties in the network, while the law of
homophily makes the network highly clustered locally and the individuals would
obtain strong and trust ties. Our findings shed light on the social network
modeling from a new perspective.
