Monopartite graph

As explained in Graph Algorithms for Data Science

A monopartite graph is a graph containing one type of node, with relationships connecting nodes within that single node set.

A monopartite graph has one class of nodes, with relationships connecting members of that same class. A friendship graph of people and friendship relationships, or a web graph of pages and hyperlinks, are common examples. This single-type structure is a practical input for many graph algorithms. section 2.1.3 section 5.1

Start by asking whether both ends of every relationship represent the same kind of thing. A Twitter follower network qualifies because every node is a User and each FOLLOWS relationship connects one user to another. Direction can still matter: one user may follow another without a reciprocal follow. Relationships may also be unweighted while retaining properties such as their creation date. section 2.3.1 section 5.1

Model a follower network

Use a User label and a specific FOLLOWS relationship, with a unique user identifier and optional registration and relationship-date properties. This yields a directed monopartite network that can be characterized by connectedness and link density, then analyzed with centrality or community-detection algorithms. section 2.3.1 section 5.1

A bipartite graph can often be projected into a monopartite graph when indirect connections are the useful analytical signal. For tweets and hashtags, connect two tweets that share a hashtag with SIMILAR relationships, or connect hashtags that co-occur. Choose the projected node type and inferred relationship meaning to fit the domain. section 2.4.2 section 7.0

A projection commonly follows these steps:

• Select one node set from a bipartite pattern, such as hashtags connected through tweets. section 2.4.2
• Infer direct relationships from the shared intermediate nodes, such as CO_OCCURRENCE between tags. section 7.0
• Optionally assign a relationship weight, such as Jaccard similarity, based on overlap between the connected sets. section 7.2.1

Figure 2.24 Monopartite network projection of a Twitter hashtag

Compare the original tweet–hashtag bipartite pattern with its projected single-type network to see how shared tags become direct connections. section 2.4.2

Projection is an analytical choice, not merely a schema rewrite. A retweet pattern can become a direct AMPLIFY relationship between users, supporting analysis of influential content creators. A mention pattern can become a co-mention network for examining communities or informing follower recommendations. section 6.0 section 2.4.3

How Graph Algorithms for Data Science covers it

How deep it goes

Defines the structure and works through projections, directedness, weighting, Cypher patterns, and Jaccard-based relationship weights.

Examples

Uses follower networks, tweet–hashtag networks, retweet amplification, user mentions, and overlapping shopping baskets.

What it assumes

Introduces the idea from basic nodes and relationships without requiring prior graph-theory expertise.

What you can do after

Apply it via Cypher to model or project single-type networks for centrality and community analysis.

How it connects

Connects bipartite graphs, graph projection, Cypher, PageRank, centrality, community detection, and Jaccard similarity.

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Also explained in

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  Knowledge Graphs and LLMs in ActionA monopartite subnetwork is a network containing one type of node, with connections only between nodes of that type.

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Related concepts

• network projectionproduced by · Network projection is the transformation of a multipartite graph into a graph containing one selected node type by inferring connections through shared neighbors.
• bipartite graphcontrasts with · A bipartite graph is a graph whose vertices can be partitioned into two disjoint sets, with edges only between the sets.
• protein-protein interaction networkhas part · A protein-protein interaction network is a graph whose nodes represent proteins and whose edges represent experimentally observed physical or functional interactions between them.
• graph algorithmused by · A graph algorithm is a computational procedure that operates on graph vertices, edges, and relationships to compute properties or solve problems.

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.