Directed graph

As explained in Graph Algorithms for Data Science

A directed network is a network whose relationships have source and target directions that can carry semantic meaning.

A directed graph represents relationships with a source and a target. Direction matters when it changes meaning: a user who follows another user receives that user’s posts, but the reverse is not implied. Unlike an undirected connection, a directed relationship supports graph-algorithm traversal in only its stated direction. section 2.1.1

Figure 2.2 (A) represents a directed graph; (B) represents an undirected graph.

Compare a one-way relationship with a connection whose direction is not essential. section 2.1.1

Model a relationship as directed when its orientation carries domain meaning. A Twitter-style follower network uses User nodes and FOLLOWS relationships: Kim following Vanessa does not mean Vanessa follows Kim. Such a network is directed and unweighted when FOLLOWS has no strength value; its creation date can still be stored as a relationship property. section 2.3.1

Follower relationship in Cypher

A directed relationship points from the follower to the followed user: (:User{id:"Vanessa", registeredAt:"2019-03-05"})-[:FOLLOWS{since:"2020-01-01"}]->(:User{id:"Thomas", registeredAt:"2011-03-05"}). The arrow records who follows whom, while properties retain registration and follow dates. section 2.3.1

Direction affects both modeling and analysis:

• Represent an undirected connection with two opposite directed relationships when traversal must work both ways. section 2.1.1
• Avoid adding an opposite duplicate relationship when direction adds no semantic value in a labeled-property graph database. section 2.5
• Use follower direction to examine direct follower counts and transitive influence, including PageRank-style influence. section 2.3.1
• Characterize a directed follower subgraph through connectedness, link density, community detection, and centrality algorithms. section 5.1

Cypher can traverse directed relationships in either direction, but that query flexibility differs from graph-algorithm input, where traversing a directed relationship backward is typically not permitted. Keep this distinction in mind when moving from exploration queries to algorithmic analysis. section 2.1.1

How Graph Algorithms for Data Science covers it

How deep it goes

Explains direction through traversal rules, Cypher modeling, and follower-network analysis without formal graph notation.

Examples

Uses Twitter-style followers, Kim and Vanessa, and a Cypher FOLLOWS relationship with date properties.

What it assumes

Teaches directed relationships from a familiar social-network example without assuming graph-theory expertise.

What you can do after

Apply it via Cypher and graph algorithms to model one-way ties and characterize follower-network structure.

How it connects

Connects directed graphs to undirected graphs, labeled-property graphs, Cypher, PageRank, community detection, and centrality.

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Related concepts

• graphkind of · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
• undirected graphcontrasts with · An undirected graph is a graph whose edges have no orientation, so each edge connects its endpoints symmetrically.
• directed acyclic graphincludes · A directed acyclic graph is a graph with directed edges and no directed cycles.
• edgehas part · An edge is a graph connection between two vertices that represents a relationship and may be directed, labeled, or weighted.
• causal graphical modelincludes · A causal graphical model is a probabilistic or structural model whose graph represents causal relationships and whose mechanisms support reasoning about interventions.
• LangGraphused by · LangGraph is a framework for building stateful, graph-structured workflows and applications, including those involving language models and agents.

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