  Great part of the interest in complex networks has been motivated by the
presence of structured, frequently non-uniform, connectivity. Because diverse
connectivity patterns tend to result in distinct network dynamics, and also
because they provide the means to identify and classify several types of
complex networks, it becomes important to obtain meaningful measurements of the
local network topology. In addition to traditional features such as the node
degree, clustering coefficient and shortest path, motifs have been introduced
in the literature in order to provide complementary description of the networks
connectivity. The current work proposes a new type of motifs, namely chains of
nodes, namely sequences of connected nodes with degree two. These chains have
been subdivided into cords, tails, rings and handles, depending on the type of
their extremities (e.g. open or connected). A theoretical analysis of the
density of such motifs in random and scale free networks is described, and an
algorithm for identifying those motifs in general networks is presented. The
potential of considering chains for network characterization has been
illustrated with respect to five categories of real-world networks including 16
cases. Several interesting findings were obtained, including the fact that
several chains were observed in the real-world networks, especially the WWW,
books, and power-grid. The possibility of chains resulting from incompletely
sampled networks is also investigated.
