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Network theory and inverse modeling are two standard tools of appliedphysics, whose combination is needed when studying the dynamical organizationof spatially distributed systems from indirect measurements. However, theassociated connectivity estimation may be affected by spatial leakage, anartifact of inverse modeling that limits the interpretability of networkanalysis. This paper investigates general analytical aspects pertaining to thisissue. First, the existence of spatial leakage is derived from the topologicalstructure of inverse operators. Then, the geometry of spatial leakage ismodeled and used to define a geometric correction scheme, which limits spatialleakage effects in connectivity estimation. Finally, this new approach fornetwork analysis is compared analytically to existing methods based on linearregressions, which are shown to yield biased coupling estimates.

Investigating complex networks with inverse models: analytical aspects of spatial leakage and connectivity estimation