# Incidence structure

This term is related to: incidence geometry
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WARNING: POTENTIAL TERMINOLOGICAL CONFUSION: Please don't confuse this with incidence system

## Definition

An incidence structure is an incidence system with two types: points and blocks.

Equivalently, it can be viewed as a bipartite graph with the two parts separated, marked, and labelled as the points versus the blocks.

## Notions

### Dual incidence structures

The dual of an incidence structure is the incidence structure obtained by interchanging the role of points and blocks. In graph-theoretic terms, it is obtained by relabelling the vertex set of points as blocks, and the vertex set of blocks as points.

### Complementary incidence structure

The complementary incidence structure to a given incidence structure is the incidence structure obtained by taking the complement of the graph associated with the incidence structure.

### Parameters

Let $v$ be the number of points and $b$ the number of blocks. We define $v_m$ as the average number of points on $m$ blocks and $b_m$ denotes the average number of blocks incident on $m$ points.