  Chimera states are a phenomenon in which order and disorder can co-exist
within a network that is fully homogeneous. Precisely how transient chimeras
emerge in finite networks of Kuramoto oscillators with phase-lag remains
unclear. Utilizing an operator-based framework to study nonlinear oscillator
networks at finite scale, we reveal the spatiotemporal impact of the adjacency
matrix eigenvectors on the Sakaguchi-Kuramoto dynamics. We identify a specific
condition for the emergence of transient chimeras in these finite networks: the
eigenvectors of the network adjacency matrix create a combination of a zero
phase-offset mode and low spatial frequency waves traveling in opposite
directions. This combination of eigenvectors leads directly to the coherent and
incoherent clusters in the chimera. This approach provides two specific
analytical predictions: (1) a precise formula predicting the combination of
connectivity and phase-lag that creates transient chimeras, (2) a mathematical
procedure for rewiring arbitrary networks to produce transient chimeras.
