# Detail: Display Subgraphs

```{figure} ../../_static/images/tetrad-interface/box-by-box/display-subgraphs.png
:name: tetrad-display-subgraphs-screenshot
:alt: Display Subgraphs dialog in the Graph box.

Display Subgraphs dialog for extracting subgraphs from a larger graph.
```

## Purpose

The **Display Subgraphs** tool is designed to help you **explore large, complicated graphs** by extracting
and visualizing **subgraphs of interest**. Instead of working with the entire graph at once, you can:

- Select a subset of variables,  
- Choose a **subgraph type** (e.g., neighbors, ancestors, paths, Markov blankets),  
- Click **Graph It!** to open a new Graph window containing only the relevant part of the graph.

This is invaluable for understanding local neighborhoods, causal families, and path structures in large graphs.

## Basic workflow

1. **Open Display Subgraphs**

   From a Graph window, choose the **Display Subgraphs** tool (for example, via the Graph menu).

2. **Select variables**

   - The dialog shows two lists:
     - **Not selected** – variables currently excluded from the subgraph,
     - **Selected** – variables currently included.
   - Use the **>** and **<** buttons to move variables between lists.
   - **Sort Variables** orders the variable names alphabetically.
   - **Text Input…** lets you specify a list of variables by name.

3. **Choose a subgraph type**

   - At the bottom, use the **graph type** drop-down to choose what kind of subgraph to construct.
   - Depending on the type, all nodes and edges that satisfy the requested relationship (adjacency, ancestry,
     path relation, degree condition, and so on) are included in the subgraph.

4. **(Optional) Degree filter**

   - For degree-based options you can specify:
     - Whether the degree should **equal**, be **at most**, or **at least** a given number,
     - The numerical threshold in the text field.

5. **Graph it**

   - Click **Graph It!** to create and display the subgraph in a new Graph window.
   - The original graph is left unchanged; you can open multiple subgraph windows for comparison.
   - Click **Done** to close the dialog when you are finished.

## Subgraph types

The graph-type drop-down offers the following subgraph types:

### Neighborhood-based selections

- **Subgraph**  
  Shows the induced subgraph on the **selected variables**: all selected nodes and all edges between them.

- **Adjacents**  
  For the selected variables, includes each selected node plus all of its **neighbors** (adjacent nodes) and
  the edges among them.

- **Adjacents of Adjacents**  
  Extends **Adjacents** one step further: includes selected nodes, their neighbors, and the neighbors of those
  neighbors.

- **Adjacents of Adjacents of Adjacents**  
  Extends the neighborhood out to three adjacency steps from the selected nodes.

### Family / causal-relation selections

- **Parents**  
  Selected nodes plus all of their **parents** and the edges between them.

- **Children**  
  Selected nodes plus all of their **children** and the edges between them.

- **Ancestors**  
  Selected nodes plus all of their **ancestors** (nodes with a directed path into them) and all connecting edges.

- **Descendants**  
  Selected nodes plus all of their **descendants** (nodes reachable by directed paths out of them) and
  the relevant edges.

- **Markov Blankets**  
  For each selected node, includes its **Markov blanket** (typically its parents, its children, and the parents
  of its children), along with all edges among these nodes.

### Path-based selections

These focus on paths and treks involving the selected variables.

- **Treks**  
  Subgraph consisting of **treks** (paths without colliders) involving the selected nodes.

- **Trek Edges**  
  Only the **edges** that lie on those treks, together with their endpoints.

- **Paths**  
  Subgraph containing **paths** involving the selected nodes.

- **Path Edges**  
  Only the **edges** that lie on such paths, together with their endpoints.

- **Directed Paths**  
  Subgraph consisting of **directed paths** involving the selected variables.

- **Directed Path Edges**  
  Only the edges that lie on those directed paths, together with their endpoints.

- **Y Structures**  
  Highlights **Y-structures** (collider patterns of the form X → Z ← Y with no edge between X and Y) that
  involve the selected variables.

- **Pag Y Structures**  
  The corresponding Y-structure patterns in **PAGs**, using PAG edge types.

### Degree-based selections

These options select nodes based on their **degree properties**.

- **Indegree**  
  Nodes whose **indegree** (number of incoming arrows) satisfies the chosen condition
  (equal / at most / at least some integer).

- **Out Degree**  
  Nodes whose **outdegree** (number of outgoing arrows) satisfies the chosen condition.

- **Degree**  
  Nodes whose **total degree** (number of incident edges, regardless of direction) satisfies the chosen condition.

In each case, you can specify the condition using the **Degree** controls at the bottom of the dialog:
**Equals**, **At Most**, or **At Least**, together with a numeric threshold.

## Summary

The **Display Subgraphs** tool lets you:

- Focus on **local neighborhoods** (adjacents and relatives),
- Examine **causal families** (parents, children, ancestors, descendants, Markov blankets),
- Study **path structures** (paths, treks, directed paths, Y-structures),
- Filter by **degree properties**.

It is especially powerful for **large graphs**, where directly seeing all of these structures in the full graph
would be difficult or impossible.