Diagrams and Tables — mermaid, tikzgraph, tikzcd, tabular

A complete guide to diagrams and tables on Folio. Covers mermaid flowcharts and sequence diagrams, tikzgraph for graph drawing, tikzcd for commutative diagrams, tabular for tables, figure/table environments, and includegraphics.

Folio Official

March 3, 2026

1. Mermaid Diagrams

Folio provides a mermaid environment for text-based diagrams. This is a Folio-specific feature not available in standard LaTeX.

1.1. Flowcharts

\begin{mermaid}
graph TD
    A[Start] --> B{Condition}
    B -->|Yes| C[Process 1]
    B -->|No| D[Process 2]
    C --> E[End]
    D --> E
\end{mermaid}

Result:

graph TD
    A[Start] --> B{Condition}
    B -->|Yes| C[Process 1]
    B -->|No| D[Process 2]
    C --> E[End]
    D --> E

1.2. Horizontal Flowcharts

Use graph LR for left-to-right flow:

\begin{mermaid}
graph LR
    A[Input] --> B[Preprocessing]
    B --> C[Model]
    C --> D[Postprocessing]
    D --> E[Output]
\end{mermaid}

Result:

graph LR
    A[Input] --> B[Preprocessing]
    B --> C[Model]
    C --> D[Postprocessing]
    D --> E[Output]

1.3. Sequence Diagrams

\begin{mermaid}
sequenceDiagram
    participant C as Client
    participant S as Server
    participant D as Database
    C->>S: HTTP Request
    S->>D: Query
    D-->>S: Result
    S-->>C: Response
\end{mermaid}

Result:

sequenceDiagram
    participant C as Client
    participant S as Server
    participant D as Database
    C->>S: HTTP Request
    S->>D: Query
    D-->>S: Result
    S-->>C: Response

1.4. Use Case: Dependency Diagrams

Useful for showing topic dependencies in textbook series:

\begin{mermaid}
graph TD
    A["Sets and Maps"] --> B["Group Definition"]
    B --> C["Subgroups"]
    B --> D["Homomorphisms"]
    C --> E["Cosets"]
    E --> F["Normal Subgroups"]
    F --> G["Quotient Groups"]
    D --> G
    G --> H["Isomorphism Theorems"]

    style A fill:#f5f5f5,stroke:#333,color:#000
    style H fill:#f5f5f5,stroke:#333,color:#000
\end{mermaid}

Result:

graph TD
    A["Sets and Maps"] --> B["Group Definition"]
    B --> C["Subgroups"]
    B --> D["Homomorphisms"]
    C --> E["Cosets"]
    E --> F["Normal Subgroups"]
    F --> G["Quotient Groups"]
    D --> G
    G --> H["Isomorphism Theorems"]

    style A fill:#f5f5f5,stroke:#333,color:#000
    style H fill:#f5f5f5,stroke:#333,color:#000

2. tikzgraph: Graph Drawing

The tikzgraph environment draws graph-theory graphs (vertices and edges). It uses a syntax unified with LaTeX notation for undirected and directed graphs. This is a Folio-specific environment.

2.1. Basic Syntax

Define vertices with id or id/$label$, connect with --, and separate edge chains with ;:

\begin{tikzgraph}
  a/$v_1$ -- b/$v_2$ -- c/$v_3$;
  a -- c;
\end{tikzgraph}

Result:

Omitting the label displays the vertex ID as-is:

\begin{tikzgraph}
  a -- b -- c;
\end{tikzgraph}

Result:

2.2. Directed Graphs

Use -> for directed edges, <- for reverse, and <-> for bidirectional:

\begin{tikzgraph}
  a/$v_1$ -> b/$v_2$ -> c/$v_3$;
  c -> a;
\end{tikzgraph}

Result:

2.3. Edge Styles and Labels

Use square brackets for edge styles (dashed, dotted, thick, double) and labels:

\begin{tikzgraph}
  a/$u$ --[dashed] b/$v$;
  a --[thick, "3"] c/$w$;
  b --[dotted] c;
\end{tikzgraph}

Result:

2.4. Layouts

Choose a layout with the environment option. Default is spring layout (force-directed); circular layout arranges vertices in a circle:

\begin{tikzgraph}[circular layout]
  a/$1$ -- b/$2$ -- c/$3$ -- d/$4$ -- e/$5$ -- a;
\end{tikzgraph}

Result:

2.5. Syntax Summary

Syntax	Meaning
`a -- b`	Undirected edge
`a -> b`	Directed edge ( $a \to b$ )
`a <- b`	Reverse edge ( $b \to a$ )
`a <-> b`	Bidirectional edge
`a/$v_1$`	Vertex $a$ with KaTeX label $v_{1}$
`--[dashed]`	Dashed style
`--[dotted]`	Dotted style
`--[thick]`	Thick style
`--[double]`	Double-line style
`--["label"]`	Edge label
`[spring layout]`	Force-directed layout (default)
`[circular layout]`	Circular layout

2.6. Multi-Edges

Defining multiple edges between the same pair automatically draws them as curves:

\begin{tikzgraph}
  A -- B; A -- B;
  A -- C; A -- C;
  A -- D;
  B -- D;
  C -- D;
\end{tikzgraph}

Result (Bridges of Kö

2.7. Subgraphs

Use {label: ...} to define subgraphs. Nodes within a subgraph are enclosed in a dashed border:

\begin{tikzgraph}
  {SCC $C_1$: a -> b -> c -> a;}
  {SCC $C_2$: d -> e -> d;}
  {SCC $C_3$: f;}
  c -> d;
  e -> f;
\end{tikzgraph}

Result:

Use {a -- b;} without a colon for an unlabeled subgraph.

2.8. Differences from Real TikZ

tikzgraph bears a TikZ-like name but is a Folio-specific simplified graph drawing environment, quite different from real TikZ:

Feature	tikzgraph	TikZ
Coordinate specification	Auto-layout only	Arbitrary coordinates
Node shapes	Circle only	Rectangle, ellipse, polygon, etc.
Color specification	Not supported	Fully customizable
Label positioning	Inside node only	above, below, left, right
Edge curves	Auto for multi-edges	bend left/right, out/in angles
`\foreach` loops	Not supported	Supported
Decorations	Not supported	snake, zigzag, etc.

Note 1.

tikzgraph is specialized for basic graph-theory graph drawing. If you need custom node shapes or colors, consider using the mermaid environment instead.

3. tikzcd: Commutative Diagrams

The tikzcd environment draws commutative diagrams, useful for category-theoretic diagrams in math articles.

3.1. Basic Commutative Diagrams

\begin{tikzcd}
A \arrow[r, "f"] \arrow[d, "g"'] & B \arrow[d, "h"] \\
C \arrow[r, "k"'] & D
\end{tikzcd}

Result:

3.2. Arrow Types

\begin{tikzcd}
A \arrow[r, "f"] & B          % Regular morphism
A \arrow[r, hookrightarrow] & B   % Injection
A \arrow[r, twoheadrightarrow] & B % Surjection
A \arrow[r, dashed] & B       % Dashed
\end{tikzcd}

Result:

3.3. Exact Sequences

A short exact sequence:

\begin{tikzcd}
0 \arrow[r] & A \arrow[r, "f"] & B \arrow[r, "g"] & C \arrow[r] & 0
\end{tikzcd}

Result:

3.4. Complex Commutative Diagrams

\begin{tikzcd}
& A \arrow[dl, "p"'] \arrow[dr, "q"] & \\
B \arrow[dr, "f"'] & & C \arrow[dl, "g"] \\
& D &
\end{tikzcd}

Result:

4. Tables (tabular Environment)

4.1. Basic Tables

\begin{tabular}{lcc}
\hline
Name & Symbol & Order \\
\hline
Cyclic group & $\mathbb{Z}/n\mathbb{Z}$ & $n$ \\
Symmetric group & $S_n$ & $n!$ \\
Dihedral group & $D_n$ & $2n$ \\
\hline
\end{tabular}

Result:

Name	Symbol	Order
Cyclic group	$Z / n Z$	$n$
Symmetric group	$S_{n}$	$n!$
Dihedral group	$D_{n}$	$2 n$

4.2. Column Alignment

Use l (left), c (center), r (right):

\begin{tabular}{|l|c|r|}
\hline
Left & Center & Right \\
\hline
apple & banana & cherry \\
dog & elephant & fox \\
\hline
\end{tabular}

Result:

Left	Center	Right
apple	banana	cherry
dog	elephant	fox

5. figure and table Environments

Use float environments for captions and numbering:

\begin{figure}
\centering
\begin{tikzcd}
A \arrow[r, "f"] \arrow[d, "g"'] & B \arrow[d, "h"] \\
C \arrow[r, "k"'] & D
\end{tikzcd}
\caption{Example of a commutative diagram}
\label{fig:commutative}
\end{figure}

Figure \ref{fig:commutative} shows the basic form of a commutative diagram.

Result:

Figure 1: Example of a commutative diagram

Figure 1 shows the basic form of a commutative diagram.

\begin{table}
\centering
\begin{tabular}{lcc}
\hline
Group & Commutativity & Finiteness \\
\hline
$(\mathbb{Z}, +)$ & Abelian & Infinite \\
$S_3$ & Non-abelian & Finite \\
$(GL_2(\mathbb{R}), \cdot)$ & Non-abelian & Infinite \\
\hline
\end{tabular}
\caption{Classification of groups}
\label{tab:groups}
\end{table}

Table \ref{tab:groups} shows a basic classification of groups.

Result:

Table 1: Classification of groups

Group	Commutativity	Finiteness
$(Z, +)$	Abelian	Infinite
$S_{3}$	Non-abelian	Finite
$(G L_{2} (R), \cdot)$	Non-abelian	Infinite

Table 1 shows a basic classification of groups.

6. Images

The \includegraphics command works if you specify an image URL directly:

\includegraphics[width=0.8\textwidth]{https://example.com/image.png}

Note 2.

Only the width option is supported. Local file paths cannot be used, so you must specify a publicly accessible URL. For creating diagrams from text, mermaid, tikzgraph, and tikzcd are recommended.

7. Summary

On Folio, you can draw text-based diagrams with mermaid (flowcharts, etc.), tikzgraph (graph-theory graphs), and tikzcd (commutative diagrams). The tabular environment for tables works as expected. Next, we'll cover cross-references, links, and custom commands.

LaTeX Folio Tutorial mermaid tikzgraph tikzcd Tables

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Mathematics "between the lines" — exploring the intuition textbooks leave out, written in LaTeX on Folio.

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Diagrams and Tables — mermaid, tikzgraph, tikzcd, tabular

1. Mermaid Diagrams

1.1. Flowcharts

1.2. Horizontal Flowcharts

1.3. Sequence Diagrams

1.4. Use Case: Dependency Diagrams

2. tikzgraph: Graph Drawing

2.1. Basic Syntax

2.2. Directed Graphs

2.3. Edge Styles and Labels

2.4. Layouts

2.5. Syntax Summary

2.6. Multi-Edges

2.7. Subgraphs

2.8. Differences from Real TikZ

3. tikzcd: Commutative Diagrams

3.1. Basic Commutative Diagrams

3.2. Arrow Types

3.3. Exact Sequences

3.4. Complex Commutative Diagrams

4. Tables (tabular Environment)

4.1. Basic Tables

4.2. Column Alignment

5. figure and table Environments

6. Images

7. Summary

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