Partial Geometry
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A figure may look like a graph, but in a graph an edge has just two ends (beyond a vertex a new edge starts), while a line in an incidence structure can be incident to more points. An incidence structure has no concept of a point being in between two other points; the order of points on a line is undefined. Compare with ordered geometry, which does have a notion of betweenness. Each hypergraph or set system can be regarded as an incidence structure in which the univer...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A figure may look like a graph, but in a graph an edge has just two ends (beyond a vertex a new edge starts), while a line in an incidence structure can be incident to more points. An incidence structure has no concept of a point being in between two other points; the order of points on a line is undefined. Compare with ordered geometry, which does have a notion of betweenness. Each hypergraph or set system can be regarded as an incidence structure in which the universal set plays the role of "points", the corresponding family of sets plays the role of "lines" and the incidence relation is set membership " ". Conversely, every incidence structure can be viewed as a hypergraph.
