  We study the influence of clustering, more specifically triangles, on
cascading failures in interdependent networks or systems, in which we model the
dependence between comprising systems using a dependence graph. First, we
propose a new model that captures how the presence of triangles in the
dependence graph alters the manner in which failures transmit from affected
systems to others. Unlike existing models, the new model allows us to
approximate the failure propagation dynamics using a multi-type branching
process, even with triangles. Second, making use of the model, we provide a
simple condition that indicates how increasing clustering will affect the
likelihood that a random failure triggers a cascade of failures, which we call
the probability of cascading failures (PoCF). In particular, our condition
reveals an intriguing observation that the influence of clustering on PoCF
depends on the vulnerability of comprising systems to an increasing number of
failed neighboring systems and the current PoCF, starting with different types
of failed systems. Our numerical studies hint that increasing clustering
impedes cascading failures under both (truncated) power law and Poisson degree
distributions. Furthermore, our finding suggests that, as the degree
distribution becomes more concentrated around the mean degree with smaller
variance, increasing clustering will have greater impact on the PoCF. A
numerical investigation of networks with Poisson and power law degree
distributions reflects this finding and demonstrates that increasing clustering
reduces the PoCF much faster under Poisson degree distributions in comparison
to power law degree distributions.
