  A network may have different types of entities and their relations. Further,
there could be additional layers of ties. The former is referred to as
Heterogeneous networks, while the latter is known as Multi-layer networks. The
present paper provides a generalized network model, namely, a Heterogeneous
Multi-layered Network (HMN), which can simultaneously be multi-layered and
heterogeneous. The model can represent homogeneous networks as well. We define
different structural measures in an HMN. We proved that the sets of all
homogeneous, heterogeneous and multi-layered networks are subsets of the set of
all HMNs. Accordingly, we established the equivalency of the proposed
structural measures of HMNs with that of homogeneous, heterogeneous, and
multi-layered networks. Following that, we show how our proposed HMN is more
efficient in tasks such as link prediction. In addition, we present a novel
parameterized algorithm (with complexity analysis) for generating synthetic
HMNs. The networks generated from our proposed algorithm are more consistent in
modelling the layer-wise degree distribution of a real-world Twitter network
(represented as HMN) than those generated by existing models. Moreover, we also
show that our algorithm is more effective in modelling an air-transportation
multiplex network when compared to an algorithm designed specifically for the
task.

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