We undertake the first formal analysis of the role of symmetry, interpreted broadly, in the design of server-centric datacenter networks. Although symmetry has been mentioned by other researchers, we explicitly relate it to various specific, structural, graph-theoretic properties of datacenter networks. Our analysis of symmetry is motivated by the need to ascertain the usefulness of a datacenter network as regards the support of network virtualization and prevalent communication patterns in multitenanted clouds. We argue that a number of structural concepts relating to symmetry from general interconnection networks, such as recursive-definability, the existence and dynamic construction of spanning trees, pancyclicity, and variations in Hamiltonicity, are appropriate topological metrics to use in this regard. In relation to symmetry, we highlight the relevance of algebraic properties and algebraic constructions within datacenter network design. Built upon our analysis of symmetry, we outline the first technique to embed guest datacenter networks in a host datacenter network that is specifically oriented towards server-centric datacenter networks. In short, we provide the graph-theoretic foundations for the design of server-centric datacenter networks so as to support network virtualization and communication patterns in cloud computing.
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