Connectivity

The connectivity display is the most structurally rich layer in the Coherence Workstation—and the most interpretively treacherous. Before reading any visualization, it helps to understand why connectivity is so hard to get right at the scalp.

Why Connectivity Is the Hardest Layer to Read

When we say two brain regions are “connected,” we’re not describing a wire. We’re describing a statistical regularity—a consistent phase relationship between the electrical oscillations recorded at two different scalp locations. That’s it. There’s no cable, no axon visible at this resolution. What we measure is a pattern of timing that suggests coordinated activity. And that distinction—between a measured relationship and an inferred connection—is what makes connectivity both powerful and dangerous.

Have you ever tried to determine who’s talking to whom in a crowded room by listening from outside the building? That’s roughly the challenge of scalp EEG connectivity. You’re measuring tiny voltage fluctuations at the scalp, each electrode capturing a mixture of signals from thousands of cortical sources blurred through cerebrospinal fluid, skull, and skin. This blurring—volume conduction—is the single biggest confound in connectivity analysis. A single cortical generator can produce correlated signals at multiple electrodes, creating the appearance of “connectivity” between regions that aren’t communicating at all.

This is why the Coherence Workstation uses the debiased weighted Phase Lag Index (dwPLI) rather than traditional coherence as its primary connectivity metric. Coherence captures all phase relationships, including zero-lag correlations—the ones most likely to reflect volume conduction rather than genuine neural communication. dwPLI, by contrast, considers only lagged phase relationships. If two signals are perfectly in sync (zero phase lag), dwPLI ignores them. The logic is straightforward: true inter-regional communication takes time to propagate, so genuine connectivity should show a consistent phase offset. Volume conduction, by definition, arrives instantaneously at all electrodes. By restricting the analysis to lagged relationships, dwPLI sacrifices some sensitivity in exchange for substantially better specificity.

But even with a robust metric, resting-state connectivity has specific vulnerabilities that you should keep in mind while reading these displays:

Artifact contamination is band-specific. Eye movements and blinks generate large electrical fields that preferentially contaminate delta connectivity, especially at frontal electrodes. Muscle tension (EMG) produces broadband high-frequency noise that masquerades as gamma connectivity. The pipeline removes artifact-laden ICA components before computing connectivity, but residual contamination is always possible. This is why the display includes explicit reliability notices on Delta and Gamma panels.

No task structure means no anchor. During a task, you can ask whether connectivity changes in response to demands—that gives you a functional handle. During rest, connectivity patterns float freely. What you’re seeing is the brain’s default organizational architecture, which is clinically meaningful but harder to contextualize. There’s no wrong answer to compare against, so interpretation relies on within-subject structure (how bands differ from each other, how hemispheres compare) rather than deviation from a task expectation.

Nineteen electrodes are not enough for spatial precision. The standard 10-20 montage provides reasonable coverage, but any attempt to interpolate continuous scalp maps from 19 points will create false spatial gradients. This is why we moved traditional connectivity topomaps behind the Advanced section—the interpolation creates a misleading impression of spatial resolution that the data doesn’t actually support. The hub-level circuit diagram and structural metrics are more honest representations of what 19 electrodes can tell you.

There is no normative connectivity database. Unlike spectral power, where normative z-scores have well-established (if debatable) reference populations, connectivity norms are essentially nonexistent for clinical use. Every connectivity finding in this display is either a within-subject comparison (left vs. right, band vs. band, rest vs. task) or a mathematically grounded property (small-world sigma, segregation index). Nothing here says “this brain is abnormal.” Everything says “this is how this brain is organized.”

How the Display Is Ordered

The visualizations are arranged to prevent premature granularity—you see the gestalt before the details:

Gestalt first: The Structural Metrics Strip gives you a single-glance snapshot. The Network Breathing Animation shows the global rhythm of connectivity across bands.
Structural layer: The Circuit Diagram reveals specific pathways. Hemispheric Balance, Small-World Topology, Network Segregation, and Frequency Topology quantify the architecture.
Contextual layer: The Rest → Task Reconfiguration Map shows adaptive flexibility. The Clinical Narrative synthesizes findings.
Detail layer: The Electrode-Level Detail section (collapsed by default) provides the raw topographic data for those who need it.

This ordering reflects a clinical reading strategy: orient to the whole, then examine the structure, then drill into specifics only when you have a reason.

Structural Metrics Strip

The metrics strip runs across the top of the connectivity display—four compact indicators that give you an immediate read on the brain’s organizational architecture before you look at any individual visualization.

Small-World σ shows the small-world index, a single number that captures whether the brain’s connectivity has the characteristic “clustered but efficient” topology found in healthy neural networks. Values above 1.5 indicate robust small-world organization; below 1.0 suggests the network has departed from this architecture. Think of it as the difference between a well-planned city (distinct neighborhoods connected by highways) and urban sprawl (everything connected to everything with no structure).

Segregation shows the global segregation index—how well the brain’s functional networks maintain their boundaries. Higher values mean networks are internally cohesive and distinct from each other. Low segregation means leaky boundaries, where networks bleed into each other. This matters because functional specialization depends on networks being able to operate somewhat independently.

Frequency Differentiation captures whether different frequency bands use different connectivity layouts. A healthy brain wires theta differently from alpha differently from beta—each band serves a different function and should have a somewhat different topology. If this value is high (meaning high similarity across bands), the brain may be using a single rigid connectivity pattern regardless of oscillatory context.

Hemispheric Symmetry shows whether left and right hemisphere connectivity strengths are reasonably balanced across bands. Mild asymmetries are normal and may reflect functional lateralization. Marked asymmetries warrant investigation.

Network Breathing Animation

The particle flow animation shows connectivity strength evolving across frequency bands as an animated cycle. Each hub region on the scalp is a node; particles flow between nodes along the strongest connections. The speed, density, and color of the particle flow encode connection strength—more particles moving faster between two hubs means stronger dwPLI coupling in that band.

As the animation cycles through bands (Delta → Theta → Alpha → Beta → Gamma), watch for:

Which connections appear and disappear. A connection that’s strong in alpha but absent in theta tells you those two regions couple in a frequency-specific way—exactly what you’d expect in a well-differentiated brain.
Whether the overall pattern changes or stays rigid. If the animation looks essentially the same in every band, the brain may lack frequency-specific functional organization. If the pattern shifts dramatically between bands, the architecture is differentiated.
The breathing rate. Slow, rhythmic changes in the overall connectivity “pulse” suggest well-organized temporal dynamics. Rapid, erratic fluctuations may indicate poor network coordination.

The animation provides a gestalt—it’s not for precise measurement. Use it to develop an intuitive sense of the connectivity landscape before examining the structural details below.

Circuit Diagram

The circuit diagram is the primary structural connectivity display. It shows the strongest functional connections between predefined hub regions for each frequency band, with bands displayed side-by-side for comparison.

Each band panel shows hub nodes (circles) connected by lines whose thickness and color encode dwPLI strength. Hubs are colored by their network membership (e.g., frontal, central, parietal, temporal, occipital networks). Only connections exceeding the significance threshold appear—weak or random connections are filtered out.

What to look for:

Band-by-band comparison. The most important clinical information comes from how the circuit changes across bands. Alpha typically shows strong posterior connectivity (occipital and parietal hubs). Theta may highlight frontal-to-posterior communication. Beta often reveals sensorimotor pathways. If a band shows an unexpected pattern—frontal dominance in alpha, or posterior dominance in beta—that’s worth investigating.
Hub prominence. A hub with many thick connections is a highly coupled region in that band. This isn’t inherently good or bad—it depends on which hub and which band. A highly coupled frontal hub in beta might reflect executive engagement; the same pattern in delta might suggest slowing.
Missing connections. Absence of expected connections is as informative as the presence of unexpected ones. If alpha shows no posterior connectivity, the brain’s dominant resting rhythm may not be organizing into the typical posterior network.

Network Summary badges appear above the circuit when enabled, showing how many networks are classified as High, Low, or Typical connectivity relative to this brain’s own distribution. This classification uses the within-network mean dwPLI, sorted into quartiles. It tells you which networks are relatively over- or under-connected, not whether they’re clinically abnormal.

Hemispheric Balance (Butterfly Chart)

The butterfly chart shows left-vs-right hemisphere connectivity for each frequency band, stacked vertically. Each row is one band, with two sets of bars:

Top bars compare the total within-hemisphere connectivity of the left and right hemispheres. The label “L+” or “R+” indicates which side dominates; “bal” means they’re balanced. This tells you whether one hemisphere has stronger internal connectivity—more tightly coupled within itself—than the other.

Bottom bars show inter-hemispheric connectivity—how strongly the two hemispheres communicate with each other at that frequency. Low inter-hemispheric bars suggest the hemispheres are operating relatively independently at that band.

Interpreting the laterality index:

Within ±0.15: Balanced—no meaningful asymmetry at this band.
±0.15 to ±0.30: Mild asymmetry—may reflect normal functional lateralization (e.g., right-hemisphere theta dominance in spatial processing) or warrant further investigation.
Beyond ±0.30: Marked asymmetry—clinically significant. Consider whether this aligns with known lateralized functions, or whether it suggests pathological asymmetry.

Small-World Topology Scatter Plot

Each dot on this scatter plot represents one frequency band. The x-axis shows the clustering ratio (γ)—how much more clustered the brain’s network is compared to a random network of the same size. The y-axis shows the path length ratio (λ)—how the brain’s average shortest path compares to random.

The green shaded region marks the “healthy” zone where σ = γ/λ > 1.5. Dots inside this zone indicate bands with robust small-world topology—the brain has both strong local neighborhoods and efficient long-range communication. Think of it as the neural equivalent of a city with distinct neighborhoods (high clustering) connected by an efficient highway system (short path lengths).

Reading the quadrants:

High γ, low λ (green zone): Small-world—the ideal architecture. Strong local clustering with efficient global communication.
Low γ, low λ (left of γ = 1): Random-like—the brain has connections but hasn’t formed meaningful local clusters in that band. The network lacks functional specialization.
High γ, high λ: Lattice-like—strong local clustering but poor long-range efficiency. The neighborhoods exist but can’t communicate efficiently across the network.
Low γ, high λ: Worst case—neither local specialization nor efficient global paths.

Threshold interpretation:

σ > 1.5: Healthy small-world organization ✓
σ 1.0–1.5: Borderline—the architecture is present but not robust ~
σ < 1.0: Departed from small-world organization ✗

Network Segregation Map

The segregation map uses a force-directed graph to visualize how well the brain’s functional networks maintain their boundaries. Each node represents a functional network (frontal, central, parietal, temporal, visual, etc.). Node size encodes how strongly the network talks to itself (within-network mean dwPLI). Lines between nodes represent between-network coupling—thicker lines mean leakier boundaries between those two networks.

Color coding:

Blue nodes are modular—they have high within-network connectivity relative to their between-network connectivity. These networks are self-contained and functionally specialized.
Amber/orange nodes are integrative—they communicate broadly with other networks. Some integration is healthy (the default mode network, for instance, naturally participates in multiple functional circuits), but excessive integration across all networks may suggest poor differentiation.

Interpreting the global segregation index:

> 1.5: Well-segregated—networks maintain clear boundaries. Healthy.
1.0–1.5: Moderate—some boundary leakage. May be normal or may warrant attention depending on which networks are leaking.
< 1.0: Poor segregation—networks are not well-differentiated. This pattern is associated with attentional and regulatory difficulties, where the brain struggles to activate one system without co-activating others.

Frequency Topology Correlation Matrix

This matrix shows how similar the connectivity topology is between each pair of frequency bands. Each cell is the Pearson correlation between two bands’ full dwPLI matrices—essentially asking: “Do these two bands wire the brain the same way?”

Color scale:

Blue/cool cells (low correlation, < 0.25): The two bands have different connectivity layouts. This is healthy—it means each frequency band serves a distinct functional role with its own wiring pattern.
Yellow/warm cells (moderate correlation, 0.25–0.50): Some shared topology. Normal for adjacent bands (e.g., Alpha1 and Alpha2 will naturally share structure).
Orange/red cells (high correlation, > 0.50): Nearly identical connectivity patterns. The brain is using the same layout for both bands, suggesting it may not be differentiating their function.

What “rigid” topology looks like: If the entire matrix is warm-colored (mean similarity > 0.50), the brain is using essentially one connectivity layout regardless of frequency. This is the structural signature of rigidity—the network can’t reorganize itself for different functional demands. A “Cannot Release” pattern in the organizational dynamics framework often shows this topology.

Healthy differentiation shows a matrix where adjacent bands share moderate structure (they’re related oscillatory processes, after all) but distant bands show low correlation (delta should wire differently from gamma).

Rest → Task Reconfiguration Map

When both resting-state and task-condition recordings are available, this visualization shows how much the brain’s connectivity pattern changes between rest and task—per band.

The reconfiguration index for each band is computed as 1 minus the correlation between the resting-state and task-state dwPLI matrices. A value of 0 means the connectivity pattern is identical in both conditions; a value of 1 means the pattern is completely different.

Interpreting reconfiguration:

Moderate reconfiguration (0.3–0.6): Healthy—the brain adapts its network topology to task demands while maintaining some structural continuity.
Very low reconfiguration (< 0.2): Suggests cognitive rigidity—the brain uses the same connectivity layout regardless of whether it’s resting or engaged. This may reflect a “Cannot Calibrate” pattern where the system doesn’t modulate in response to demands.
Very high reconfiguration (> 0.7): Suggests instability—the network topology changes so dramatically between conditions that it may reflect poor network maintenance rather than adaptive flexibility.

The display also identifies which networks change the most and which change the least between conditions, highlighting where adaptive flexibility or rigidity is concentrated.

Clinical Narrative Summary

The clinical narrative is a machine-generated synthesis of the connectivity findings. It identifies key patterns across the structural metrics, highlights notable asymmetries or departures from expected organization, and suggests clinical implications.

This summary is a starting point for interpretation, not a conclusion. It aggregates the quantitative findings into prose, but the clinician’s job is to contextualize these patterns against the patient’s clinical history, symptom presentation, and findings from other analysis layers (spectral, microstate, ERP).

The narrative typically includes:

A headline summarizing the dominant organizational pattern
Key findings ranked by clinical significance (notable, significant, or critical)
Clinical implications linking connectivity patterns to potential functional consequences

Electrode-Level Detail (Advanced)

The advanced section (collapsed by default) provides electrode-level connectivity topomaps—the raw, per-electrode connectivity data that underlies the hub-level summaries above.

These topomaps show node strength (total connectivity per electrode) and coherence strength as interpolated scalp maps. They’re useful for investigating specific electrode-level questions, but they should be read with caution: the interpolation from 19 electrodes creates smooth gradients that may suggest spatial precision the data doesn’t actually support.

When to use the advanced view:

You’ve identified a pattern in the circuit diagram or structural metrics and want to verify it at the electrode level
You need to examine a specific electrode pair’s connectivity
You want to compare the dwPLI and coherence views for the same data (coherence is included here because some clinicians are more familiar with it, even though dwPLI is the more robust measure)

When not to rely on it:

For initial interpretation—start with the hub-level views
For spatial localization claims—19-electrode interpolation is not sufficient for precise localization
As the primary connectivity display—the structural metrics provide more clinically useful information