Unweighted graph

As explained in Graph Algorithms for Data Science

An unweighted graph is a graph in which all relationships have the same strength or traversal cost and no relationship weight distinguishes them.

An unweighted graph treats every relationship as having the same strength or traversal cost. It does not distinguish stronger from weaker connections with numeric weights. section 2.1.2

Whether relationships are directed is a separate modeling choice. A graph can have equal-cost relationships while still preserving who follows whom. section 5.1

When modeling an unweighted network, decide:

• Which entities become nodes and which interaction becomes the relationship. section 2.3.1
• Whether relationship direction carries meaning, such as one user following another without reciprocal following. section 2.3.1 section 5.1
• Whether a property quantifies relationship strength; without such a property, the network remains unweighted. section 5.1

Twitter follower network

Represent users as User nodes and follows as directed FOLLOWS relationships. Because the relationships do not quantify strength, the follower network is directed and unweighted. Its structure can then be characterized through connectedness, link density, community detection, and centrality algorithms. section 2.3.1 section 5.1

Figure 2.4 (A) represents an unweighted graph; (B) represents a weighted graph.

Compare an unweighted graph, where all relationships have equal cost, with a weighted graph, where numeric attributes express strength or traversal cost. section 2.1.2

How Graph Algorithms for Data Science covers it

How deep it goes

Defines equal relationship cost, contrasts numeric weights, and applies the distinction to a directed follower network.

Examples

Uses a Twitter follower network with User nodes and directed FOLLOWS relationships lacking strength attributes.

What it assumes

Builds from nodes, relationships, labels, properties, identifiers, and relationship direction through a follower-network modeling task.

What you can do after

Apply it via Cypher and Neo4j Graph Data Science algorithms to characterize connectedness, density, communities, and centrality.

How it connects

Connects unweighted graphs with weighted graphs, directed networks, monopartite networks, community detection, and centrality.

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Also explained in

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Related concepts

• weighted graphcontrasts with · A weighted graph is a graph whose edges have associated values representing quantities such as cost, distance, strength, or frequency.
• graphkind of · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
• adjacency matrixuses · An adjacency matrix is a square matrix whose rows and columns represent graph vertices and whose entries indicate edges or encode edge weights between vertex pairs.
• breadth-first searchused by · Breadth-first search is a graph or tree traversal algorithm that explores nodes in nondecreasing order of their distance from a starting node.
• unweighted edgehas part · A graph edge that represents a connection without an associated weight.

This explainer was generated by Manning's knowledge graph from the text of Graph Algorithms for Data Science. The section links point to the parts of the book it draws on.