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Hypergraph is like a graph but one where vertexes can connect more than two nodes. Right? Isn't that just like the difference between Object Oriented and Rela

Hypergraph is like a graph but one where vertexes can connect more than two nodes. Right? Isn't that just like the difference between Object Oriented and Relational, Models? A relational table has multiple columns. A relational table does not represent a relation between two things. It represents a relation between N things, with its N columns.

lmeyerov 4y ago
Yep, close -- it's where an edge can connect more than 2 nodes Two things to make this way more intuitive & practical: * Modeling: We use them for helping folks correlate across events, or correlating across wide database rows. Ex: Finding bots & fraudsters in your signup events or accounts table . A signup event might have the same weird User Agent, same weird IP, same weird domain name, etc: its good to see events connected across multiple such things! So any time you have an event or a wide row, you can think of it as a hyperedge connecting (correlating) the multiple entities involved. * Visualizing: It's typically weird visually to draw an edge connecting more than 2 nodes, so most people don't. Instead, sometimes, our users want to see a correlation event as an explicit node in a graph. SO there's a natural bipartite graph from events to entities, like "(signup)-> (user agent)" + "(signup)->(ip)" + ... . But other times its annoying, so they rather just see "(ip:node)<-[signup:edge]-->(useragent:node)". Interestingly, for really wide data, having an explicit "hypernode" (event node) does increase the number of nodes... but significantly decreases the number of edges b/c avoids drawing really big connected components. Formally, add |events| nodes, vs multiply edges by |number of columns|^2 . If you want to play with it, try "graphistry.hypergraph(pd.read_csv('http://blah.csv'))['graph'].plot http://blah.csv'))['graph'].plot()" in http://github.com/graphistry/pygraphistry http://github.com/graphistry/pygraphistry (or just to get the ._nodes and ._edges dataframes out) Nowdays, we also do a lot with embedding arbitrary data and exploring similarity graphs that way (use k-nn for inferring similarity edges), so not just across entity links but also say timestamps, $'s, and byte counts. Any dataset embedding can thus be thought of as a projection of the hypergraph, and supporting more interesting columns than just entity columns (categoricals). So in the above example, `graphistry.nodes(pd.read_csv('http://blah.csv')).umap().plot http://blah.csv')).umap().plot()` and we'll infer the `._edges`. All the nodes in an embedding view are essentially hypernodes, and instead of connecting them to entity/attribute nodes... project those out, and just connect the hypernodes to one another. This gives a very different way to think about stuff like explainability of AI :)
nighthawk454 4y ago
Yes, a hyperedge is like a set of nodes. Not limited to just two nodes. I hadn't thought of relational tables in that way. I guess, you could look at each row of a table as a hyperedge grouping together all the columns for a given record. Not sure how useful that is though. The cross-table join relations are still relatively point-to-point I think.
- galaxyLogic 4y ago
  It might be just a good way of thinking about it. In practice it might provide some ideas about how to translate between an Object-view and Relational-View. What I'd like to find is a relational database where field-values can be not just elementary values like numbers and strings but also "object-instances". I wonder is there such a database? It would seem to offer the best of both worlds, objects, and relations between objects.
  - nighthawk454 4y ago
    This might not be quite it, but perhaps you’re looking for graph databases?
    - galaxyLogic 4y ago
      Can you use SQL with graph databases? Related to the current topic, do graph databases support hyper-graphs?
      - nighthawk454 4y ago
        I don't believe they support SQL. They're somewhat more like pattern-matching on graphs. Most of their query language pages have compare/contrast examples with an equivalent SQL query. e.g. Neo4j's Cypher query language [1], or Apache Tinkerpop Gremlin (seriously) [2] used by Amazon Neptune. I don't think the most popular ones support hypergraphs, although that sounds cool. I did see HypergraphDB [3] though! Need to read more about that. [1] https://neo4j.com/developer/cypher/guide-sql-to-cypher/#cypher-sql-northwind https://neo4j.com/developer/cypher/guide-sql-to-cypher/#cyph... [2] https://tinkerpop.apache.org/gremlin.html#:~:text=Host%20Language%20Embedding https://tinkerpop.apache.org/gremlin.html#:~:text=Host%20Lan... [3] http://hypergraphdb.org/ http://hypergraphdb.org/
deleted 4y ago
[deleted]
mnd999 4y ago
This can be modelled as a regular graph simply by representing the hyper edge as another node with a set of edges. If those are labelled appropriately to differentiate them from regular nodes, it’s straightforward enough to represent it as a regular graph.
- nine_k 4y ago
  Many things can be represented as more complex structures of simpler things. It's interesting whether a new formalism allows to express things better, unearth interesting structures not apparent using a more busy formalism, etc. Compare the Maxwell equations in the wordy original form, and in a highly compact Clifford algebra form.
- galaxyLogic 4y ago
  Right but doesn't that mean that in essence you will have two types of nodes in your conceptual model. It is no longer that you have just 'nodes' and 'vertices', you will need to have two different types of nodes, and one type of vertex. The new type of node could be called 'hyper-node' perhaps. Else you lose information.

lmeyerov 4y ago

Yep, close -- it's where an edge can connect more than 2 nodes Two things to make this way more intuitive & practical: * Modeling: We use them for helping folks correlate across events, or correlating across wide database rows. Ex: Finding bots & fraudsters in your signup events or accounts table . A signup event might have the same weird User Agent, same weird IP, same weird domain name, etc: its good to see events connected across multiple such things! So any time you have an event or a wide row, you can think of it as a hyperedge connecting (correlating) the multiple entities involved. * Visualizing: It's typically weird visually to draw an edge connecting more than 2 nodes, so most people don't. Instead, sometimes, our users want to see a correlation event as an explicit node in a graph. SO there's a natural bipartite graph from events to entities, like "(signup)-> (user agent)" + "(signup)->(ip)" + ... . But other times its annoying, so they rather just see "(ip:node)<-[signup:edge]-->(useragent:node)". Interestingly, for really wide data, having an explicit "hypernode" (event node) does increase the number of nodes... but significantly decreases the number of edges b/c avoids drawing really big connected components. Formally, add |events| nodes, vs multiply edges by |number of columns|^2 . If you want to play with it, try "graphistry.hypergraph(pd.read_csv('http://blah.csv'))['graph'].plot http://blah.csv'))['graph'].plot()" in http://github.com/graphistry/pygraphistry http://github.com/graphistry/pygraphistry (or just to get the ._nodes and ._edges dataframes out) Nowdays, we also do a lot with embedding arbitrary data and exploring similarity graphs that way (use k-nn for inferring similarity edges), so not just across entity links but also say timestamps, $'s, and byte counts. Any dataset embedding can thus be thought of as a projection of the hypergraph, and supporting more interesting columns than just entity columns (categoricals). So in the above example, `graphistry.nodes(pd.read_csv('http://blah.csv')).umap().plot http://blah.csv')).umap().plot()` and we'll infer the `._edges`. All the nodes in an embedding view are essentially hypernodes, and instead of connecting them to entity/attribute nodes... project those out, and just connect the hypernodes to one another. This gives a very different way to think about stuff like explainability of AI :)

nighthawk454 4y ago

Yes, a hyperedge is like a set of nodes. Not limited to just two nodes. I hadn't thought of relational tables in that way. I guess, you could look at each row of a table as a hyperedge grouping together all the columns for a given record. Not sure how useful that is though. The cross-table join relations are still relatively point-to-point I think.

galaxyLogic 4y ago
It might be just a good way of thinking about it. In practice it might provide some ideas about how to translate between an Object-view and Relational-View. What I'd like to find is a relational database where field-values can be not just elementary values like numbers and strings but also "object-instances". I wonder is there such a database? It would seem to offer the best of both worlds, objects, and relations between objects.
- nighthawk454 4y ago
  This might not be quite it, but perhaps you’re looking for graph databases?
  - galaxyLogic 4y ago
    Can you use SQL with graph databases? Related to the current topic, do graph databases support hyper-graphs?
    - nighthawk454 4y ago
      I don't believe they support SQL. They're somewhat more like pattern-matching on graphs. Most of their query language pages have compare/contrast examples with an equivalent SQL query. e.g. Neo4j's Cypher query language [1], or Apache Tinkerpop Gremlin (seriously) [2] used by Amazon Neptune. I don't think the most popular ones support hypergraphs, although that sounds cool. I did see HypergraphDB [3] though! Need to read more about that. [1] https://neo4j.com/developer/cypher/guide-sql-to-cypher/#cypher-sql-northwind https://neo4j.com/developer/cypher/guide-sql-to-cypher/#cyph... [2] https://tinkerpop.apache.org/gremlin.html#:~:text=Host%20Language%20Embedding https://tinkerpop.apache.org/gremlin.html#:~:text=Host%20Lan... [3] http://hypergraphdb.org/ http://hypergraphdb.org/

deleted 4y ago

[deleted]

mnd999 4y ago

This can be modelled as a regular graph simply by representing the hyper edge as another node with a set of edges. If those are labelled appropriately to differentiate them from regular nodes, it’s straightforward enough to represent it as a regular graph.

nine_k 4y ago
Many things can be represented as more complex structures of simpler things. It's interesting whether a new formalism allows to express things better, unearth interesting structures not apparent using a more busy formalism, etc. Compare the Maxwell equations in the wordy original form, and in a highly compact Clifford algebra form.
galaxyLogic 4y ago
Right but doesn't that mean that in essence you will have two types of nodes in your conceptual model. It is no longer that you have just 'nodes' and 'vertices', you will need to have two different types of nodes, and one type of vertex. The new type of node could be called 'hyper-node' perhaps. Else you lose information.