Spatio-Temporal Graphs

What is a Spatio-Temporal Graph?

A spatio-temporal graph (STG) is a directed graph that models how brain connectivity evolves over time. Each node in the graph represents a brain area at a specific time point, and edges encode two distinct types of relationships:

  • Spatial edges — connect two brain areas at the same time point when their correlation exceeds the threshold. They represent synchronous functional connectivity.

  • Temporal edges — connect a brain area (or group of areas) across consecutive time points, labelled with an RC5 transition type. They encode how connectivity patterns change over time.

This representation unifies the spatial structure of brain connectivity with its temporal dynamics into a single graph object, enabling both snapshot-level and longitudinal analyses.

Graph Structure

Formally, a spatio-temporal graph G = (V, E_s ∪ E_t) where:

  • V is the set of nodes. Each node v = (area, time) uniquely identifies a brain area at a given time step.

  • E_s ⊆ V × V is the set of spatial edges. An edge (u, v) ∈ E_s exists when both nodes share the same time step and their Pearson correlation exceeds the configured threshold.

  • E_t ⊆ V × V is the set of temporal edges. An edge (u, v) ∈ E_t connects nodes at consecutive time steps and carries an RC5 transition label.

The SpatioTemporalGraph Class

In fSTG Toolkit, STGs are represented by the fstg_toolkit.graph.SpatioTemporalGraph class, which extends networkx.DiGraph. This means the full NetworkX API is available for querying and manipulating the graph.

Key graph-level attributes stored in graph.graph:

  • max_time — the index of the last time step

  • areas — the list of brain area identifiers

Node attributes include:

  • time — the time step index

  • area — the brain area identifier

  • region — the region this area belongs to

Edge attributes include:

  • type — "spatial" or "temporal"

  • rc5 — the fstg_toolkit.graph.RC5 transition label (temporal edges only)

  • correlation — the Pearson correlation value (spatial edges only)

From Correlation Matrices to Graphs

The factory function fstg_toolkit.factory.spatio_temporal_graph_from_corr_matrices() converts a sequence of correlation matrices into an STG:

  1. For each time step t, the (N × N) correlation matrix is thresholded. Pairs of areas whose absolute correlation exceeds the threshold are connected by a spatial edge.

  2. For each pair of consecutive time steps t and t+1, the connectivity patterns of each area are compared and an RC5 transition label is assigned to the temporal edge.

Building is parallelised across subjects via ProcessPoolExecutor.

Use Cases

Spatio-temporal graphs are well suited for:

  • Longitudinal analysis — tracking how connectivity reorganises across sessions, disease stages, or experimental conditions.

  • Group comparison — comparing graph metrics between patient groups and healthy controls.

  • Pattern discovery — finding recurring subgraph patterns that appear across multiple subjects using frequent subgraph mining.