  Network data, characterized by interconnected nodes and edges, is pervasive
in various domains and has gained significant popularity in recent years. In
network data analysis, testing the presence of community structure in a network
is one of the important research tasks. Existing tests are mainly developed for
unweighted networks. In this paper, we study the problem of testing the
existence of community structure in general (either weighted or unweighted)
networks. We propose two new tests: the Weighted Signed-Triangle (WST) test and
the empirical likelihood (EL) test. Both tests can be applied to weighted or
unweighted networks and outperform existing tests for small networks. The EL
test may outperform the WST test for small networks.
