What are the right mathematical tools / language to analyse complex networks over time?

Question

In this article about human physiology as a complex network the authors say that:

"Lacking adequate analytic tools and a theoretical framework to probe interactions within and among diverse physiological systems, current approaches focus on inferring properties of time-varying interactions—namely strength, direction, and functional form—from time-locked recordings of physiological observables."

and further:

The characterization of interactions between physiological systems faces several challenges:

• We often do not know exactly the systems’ equations of motion;

• We lack knowledge as to how to merge/combine these equations (e.g., due to the issue of time-scale matching);

• We may have insufficient knowledge about relevant structural connections; • We may not have direct access to interactions between systems (e.g., via probing).

Image taken from the above article, where each node corresponds to a human organ and connections between organs represent time varying "connections":

Are there tools of complex networks from mathematical point of view which might be suited for the case written above?

Answer 1

There may well be suitable proprietary tools, but if you prefer open source, you might try Cytoscape.

Cytoscape is an open source software platform for visualizing molecular interaction networks and biological pathways and integrating these networks with annotations, gene expression profiles and other state data.

This Google Scholar list gives you an overview of publications that use this tool.