Network structure from a characterization of interactions in complex systems

Abstract

Many natural and man-made complex dynamical systems can be represented by networks with vertices representing system units and edges the coupling between vertices. If edges of such a structural network are inaccessible, a widely used approach is to identify them with interactions between vertices, thereby setting up a functional network. However, it is an unsolved issue if and to what extent important properties of a functional network on the global and the local scale match those of the corresponding structural network. We address this issue by deriving functional networks from characterizing interactions in paradigmatic oscillator networks with widely-used time-series-analysis techniques for various factors that alter the collective network dynamics. Surprisingly, we find that particularly key constituents of functional networks—as identified with betweenness and eigenvector centrality—coincide with ground truth to a high degree, while global topological and spectral properties—clustering coefficient, average shortest path length, assortativity, and synchronizability—clearly deviate. We obtain similar concurrences for an empirical network. Our findings are of relevance for various scientific fields and call for conceptual and methodological refinements to further our understanding of the relationship between structure and function of complex dynamical systems.

Beta-cell Metabolic Activity Rather than Gap Junction Structure Dictates Subpopulations in the Islet Functional Network

“…Therefore, the understanding that synchronization can give insight into cellular properties that drive excitability of the cell can be useful in many systems. Our results also show that forming structurally-based conclusions about a network using the functional network should be done with caution (we refer to 20 ).…”

“…Finally, removal of gap junctions, as occurs in diabetes, caused decreases in the efficiency and clustering of the functional network. These results indicate that metabolism rather than structure drives connections in the function network, deepening our interpretation of functional networks and the formation of functional sub-populations in dynamic tissues such as the islet.dynamics assume that the functional network directly reflects the structural network, which is not always true 17,20 . This leads to our second question: what does the islet functional network indicate about its underlying structure or intrinsic cell properties on an individual cell basis?…”

“…We hypothesize that this distinction may clarify whether β -cell hubs influence islet dynamics by dominating electrical communication. Further, the debates around islet heterogeneity and dynamics assume that the functional network directly reflects the structural network, which is not always true 17,20 . This leads to our second question: what does the islet functional network indicate about its underlying structure or intrinsic cell properties on an individual cell basis?…”

“…Network analysis can quantify the relationships between interacting parts of a system [13][14][15][16][17] ; represented by its entities (nodes) and their interactions (edges). In the islet, nodes can correspond to 𝛽-cells, while edges represent either structural or functional relationships [17][18][19][20] . Structural networks represent physical connections, such as gap junctions.…”

“…dynamics assume that the functional network directly reflects the structural network, which is not always true 17,20 . This leads to our second question: what does the islet functional network indicate about its underlying structure or intrinsic cell properties on an individual cell basis?…”