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This paper uses the reliability polynomial, introduced by Moore and Shannon in 1956, to analyze the effect of network structure on diffusive dynamics such as the spread of infectious disease. We exhibit a representation for the reliability polynomial in terms of what we call {em structural motifs} that is well suited for reasoning about the effect of a networks structural properties on diffusion across the network. We illustrate by deriving several general results relating graph structure to dynamical phenomena.
Investigating the frequency and distribution of small subgraphs with a few nodes/edges, i.e., motifs, is an effective analysis method for static networks. Motif-driven analysis is also useful for temporal networks where the spectrum of motifs is sign
The structure of nanoclusters is complex to describe due to their noncrystallinity, even though bonding and packing constraints limit the local atomic arrangements to only a few types. A computational scheme is presented to extract coordination motif
Higher-order proximity (HOP) is fundamental for most network embedding methods due to its significant effects on the quality of node embedding and performance on downstream network analysis tasks. Most existing HOP definitions are based on either hom
Cellular processes do not follow deterministic rules; even in identical environments genetically identical cells can make random choices leading to different phenotypes. This randomness originates from fluctuations present in the biomolecular interac
The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of networks and t