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Connectivity Metric Ranges

The following summarizes the theoretical value ranges for common connectivity metrics.

Metric Range Notes
Power [0, ∞) Power spectral density; always non-negative.
Coherency (complex) |C_{xy}(f)| ∈ [0, 1]; phase ∈ [−π, π] Values lie in the unit disk of the complex plane.
Coherence phase [−π, π] Phase angles of complex coherency.
Coherence magnitude [0, 1] 0: none; 1: perfect linear dependence at frequency f.
Imaginary coherence [0, 1] (magnitude) Raw imaginary part ranges [−1, 1]; magnitude version.
Canonical coherence [0, 1] Maximal coherence between groups.
Global coherence [0, ∞) Squared singular values; no upper bound.
PLV (Phase‑Locking Value) [0, 1] 0: random phases; 1: constant phase diff.
PLI (Phase‑Lag Index) [−1, 1] Signed version; unsigned in [0, 1].
wPLI (Weighted PLI) [0, 1] Weights by |Im(Sxy)|.
dwPLI (Debiased PLI²) [0, 1] Bias‑corrected squared PLI.
dwPLI² (Debiased squared wPLI) [0, 1] Bias‑corrected weighted PLI squared.
PPC (Pairwise Phase Consistency) [0, 1] Unbiased phase consistency; bounded as PLV.
Spectral Granger causality [0, ∞) Non‑negative; no finite upper bound.
DTF (Directed Transfer Function) [0, 1] (normalized) Proportion of inflow via transfer function.
Directed coherence [0, 1] (normalized) DTF scaled by noise variance.
PDC (Partial Directed Coherence) [0, 1] (normalized) Directional influence via AR coefficients.
gPDC (Generalized PDC) [0, 1] (normalized) PDC scaled by noise variance.
dDTF (Direct DTF) [0, 1] (normalized) DTF with partial coherence normalization.
Group delay (−∞, ∞) Time delays; can be positive or negative.
PSI (Phase Slope Index) (−∞, ∞) Signed; magnitude depends on phase slope.

Notes

  • For metrics bounded in [0, 1], numerical implementations should clamp to the interval after computation to avoid tiny overflows (e.g., 1 ± 1e−12).
  • For phase‑based metrics, choose an expectation (sample) axis (trials/tapers/segments) and aggregate only across that axis.
  • Document the shapes/dtypes of inputs and outputs in each docstring per NumPy style.
  • Also document that for granger causality output [i,j] (row i, column j) corresponds to j --> i.

Implementation Details

Bounded Metrics [0, 1]

  • coherence_magnitude: Magnitude-squared coherence
  • imaginary_coherence: Magnitude of imaginary coherency
  • canonical_coherence: Maximal coherence between groups
  • phase_locking_value: Phase consistency measure
  • weighted_phase_lag_index: Weighted by imaginary coherency magnitude
  • debiased_squared_phase_lag_index: Bias-corrected squared PLI
  • debiased_squared_weighted_phase_lag_index: Bias-corrected wPLI²
  • pairwise_phase_consistency: Unbiased phase consistency
  • directed_transfer_function: Normalized directional influence
  • directed_coherence: DTF scaled by noise variance
  • partial_directed_coherence: Normalized causal influence
  • generalized_partial_directed_coherence: PDC scaled by noise variance
  • direct_directed_transfer_function: DTF with partial coherence normalization

Bounded Metrics [−1, 1]

  • phase_lag_index: Signed phase consistency (unsigned version in [0, 1])

Phase Metrics [−π, π]

  • coherence_phase: Phase angles of complex coherency

Unbounded Metrics [0, ∞)

  • power: Power spectral density
  • global_coherence: Squared singular values
  • pairwise_spectral_granger_prediction: Spectral Granger causality

Unbounded Metrics (−∞, ∞)

  • group_delay: Time delays between signals
  • phase_slope_index: Directional phase coupling measure

Complex-valued Metrics

  • coherency: Complex coherence with magnitude ∈ [0, 1] and phase ∈ [−π, π]