  Leveraging generative Artificial Intelligence (AI), we have transformed a
dataset comprising 1,000 scientific papers into an ontological knowledge graph.
Through an in-depth structural analysis, we have calculated node degrees,
identified communities and connectivities, and evaluated clustering
coefficients and betweenness centrality of pivotal nodes, uncovering
fascinating knowledge architectures. The graph has an inherently scale-free
nature, is highly connected, and can be used for graph reasoning by taking
advantage of transitive and isomorphic properties that reveal unprecedented
interdisciplinary relationships that can be used to answer queries, identify
gaps in knowledge, propose never-before-seen material designs, and predict
material behaviors. We compute deep node embeddings for combinatorial node
similarity ranking for use in a path sampling strategy links dissimilar
concepts that have previously not been related. One comparison revealed
structural parallels between biological materials and Beethoven's 9th Symphony,
highlighting shared patterns of complexity through isomorphic mapping. In
another example, the algorithm proposed a hierarchical mycelium-based composite
based on integrating path sampling with principles extracted from Kandinsky's
'Composition VII' painting. The resulting material integrates an innovative set
of concepts that include a balance of chaos/order, adjustable porosity,
mechanical strength, and complex patterned chemical functionalization. We
uncover other isomorphisms across science, technology and art, revealing a
nuanced ontology of immanence that reveal a context-dependent heterarchical
interplay of constituents. Graph-based generative AI achieves a far higher
degree of novelty, explorative capacity, and technical detail, than
conventional approaches and establishes a widely useful framework for
innovation by revealing hidden connections.
