  In the course of the growth of the Internet and due to increasing
availability of data, over the last two decades, the field of network science
has established itself as an own area of research. With quantitative scientists
from computer science, mathematics, and physics working on datasets from
biology, economics, sociology, political sciences, and many others, network
science serves as a paradigm for interdisciplinary research. One of the major
goals in network science is to unravel the relationship between topological
graph structure and a network's function. As evidence suggests, systems from
the same fields, i.e. with similar function, tend to exhibit similar structure.
However, it is still vague whether a similar graph structure automatically
implies likewise function. This dissertation aims at helping to bridge this
gap, while particularly focusing on the role of triadic structures. After a
general introduction to the main concepts of network science, existing work
devoted to the relevance of triadic substructures is reviewed. A major
challenge in modeling such structure is the fact that not all three-node
subgraphs can be specified independently of each other, as pairs of nodes may
participate in multiple triadic subgraphs. In order to overcome this obstacle,
a novel class of generative network models based on pair-disjoint triadic
building blocks is suggested. It is further investigated whether triad motifs -
subgraph patterns which appear significantly more frequently than expected at
random - occur homogeneously or heterogeneously distributed over graphs.
Finally, the influence of triadic substructure on the evolution of dynamical
processes acting on their nodes is studied. It is observed that certain motifs
impose clear signatures on the systems' dynamics, even when embedded in a
larger network structure.
