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hypergraphs

A hypergraph is a generalization of a graph in which an edge can connect any number of vertices, rather than just two. This concept was introduced by Claude Berge in 1973. In a hypergraph, an edge is often referred to as a hyperedge, and it can be represented as a subset of the vertex set. Hypergraphs are used in various fields such as computer science, social network analysis, and operations research.

Hypergraphs can be represented using an incidence matrix, where rows correspond to vertices and columns correspond

Hypergraphs have several properties that are not present in simple graphs. For example, a hypergraph can have

Hypergraphs are used in various applications, such as in the study of social networks, where a hyperedge

to
hyperedges.
An
entry
in
the
matrix
is
1
if
the
vertex
is
incident
to
the
hyperedge,
and
0
otherwise.
Another
common
representation
is
the
bipartite
graph,
where
one
set
of
vertices
represents
the
vertices
of
the
hypergraph,
and
the
other
set
represents
the
hyperedges.
multiple
edges
connecting
the
same
set
of
vertices,
and
it
can
also
have
loops,
which
are
hyperedges
that
connect
a
single
vertex
to
itself.
Hypergraphs
can
also
be
directed,
where
the
direction
of
the
hyperedge
is
important.
can
represent
a
group
of
people
who
are
all
friends
with
each
other.
They
are
also
used
in
operations
research
for
modeling
problems
such
as
facility
location
and
scheduling.
In
computer
science,
hypergraphs
are
used
in
the
study
of
database
systems
and
in
the
design
of
algorithms
for
graph
problems.