Chain motifs: The tails and handles of complex networks
Paulino R. Villas Boas, Francisco A. Rodrigues, Gonzalo Travieso and, Luciano da F. Costa

TL;DR
This paper introduces a new class of network motifs called chains, analyzes their density in different networks, and demonstrates their usefulness in characterizing real-world complex networks.
Contribution
It proposes a novel motif type based on chains of degree-two nodes, along with an algorithm for their detection and analysis in various networks.
Findings
Chains are prevalent in real-world networks like WWW, books, and power grids.
Theoretical analysis of chain density in random and scale-free networks.
Chains can result from incomplete sampling of networks.
Abstract
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…
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