ACM Computing Surveys,
Journal Year:
2025,
Volume and Issue:
unknown
Published: Feb. 20, 2025
Hypergraphs,
which
belong
to
the
family
of
higher-order
networks,
are
a
natural
and
powerful
choice
for
modeling
group
interactions
in
real
world.
For
example,
when
collaboration
may
involve
not
just
two
but
three
or
more
people,
use
hypergraphs
allows
us
explore
beyond
pairwise
(dyadic)
patterns
capture
groupwise
(polyadic)
patterns.
The
mathematical
complexity
offers
both
opportunities
challenges
hypergraph
mining.
goal
mining
is
find
structural
properties
recurring
real-world
across
different
domains,
we
call
To
patterns,
need
tools.
We
divide
tools
into
categories:
(1)
null
models
(which
help
test
significance
observed
patterns),
(2)
elements
(i.e.,
substructures
such
as
open
closed
triangles),
(3)
quantities
numerical
computing
transitivity).
There
also
generators,
whose
objective
produce
synthetic
that
faithful
representation
hypergraphs.
In
this
survey,
provide
comprehensive
overview
current
landscape
mining,
covering
tools,
generators.
taxonomies
each
offer
in-depth
discussions
future
research
on
Physics Reports,
Journal Year:
2020,
Volume and Issue:
874, P. 1 - 92
Published: June 13, 2020
The
complexity
of
many
biological,
social
and
technological
systems
stems
from
the
richness
interactions
among
their
units.
Over
past
decades,
a
great
variety
complex
has
been
successfully
described
as
networks
whose
interacting
pairs
nodes
are
connected
by
links.
Yet,
in
face-to-face
human
communication,
chemical
reactions
ecological
systems,
can
occur
groups
three
or
more
cannot
be
simply
just
terms
simple
dyads.
Until
recently,
little
attention
devoted
to
higher-order
architecture
real
systems.
However,
mounting
body
evidence
is
showing
that
taking
structure
these
into
account
greatly
enhance
our
modeling
capacities
help
us
understand
predict
emerging
dynamical
behaviors.
Here,
we
present
complete
overview
field
beyond
pairwise
interactions.
We
first
discuss
methods
represent
give
unified
presentation
different
frameworks
used
describe
highlighting
links
between
existing
concepts
representations.
review
measures
designed
characterize
models
proposed
literature
generate
synthetic
structures,
such
random
growing
simplicial
complexes,
bipartite
graphs
hypergraphs.
introduce
rapidly
research
on
topology.
focus
novel
emergent
phenomena
characterizing
landmark
processes,
diffusion,
spreading,
synchronization
games,
when
extended
elucidate
relations
topology
properties,
conclude
with
summary
empirical
applications,
providing
an
outlook
current
conceptual
frontiers.
Journal of The Royal Society Interface,
Journal Year:
2022,
Volume and Issue:
19(188)
Published: March 1, 2022
Network
science
has
evolved
into
an
indispensable
platform
for
studying
complex
systems.
But
recent
research
identified
limits
of
classical
networks,
where
links
connect
pairs
nodes,
to
comprehensively
describe
group
interactions.
Higher-order
a
link
can
more
than
two
have
therefore
emerged
as
new
frontier
in
network
science.
Since
interactions
are
common
social,
biological
and
technological
systems,
higher-order
networks
recently
led
important
discoveries
across
many
fields
research.
Here,
we
review
these
works,
focusing
particular
on
the
novel
aspects
dynamics
that
emerges
networks.
We
cover
variety
dynamical
processes
thus
far
been
studied,
including
different
synchronization
phenomena,
contagion
processes,
evolution
cooperation
consensus
formation.
also
outline
open
challenges
promising
directions
future
Nature Communications,
Journal Year:
2023,
Volume and Issue:
14(1)
Published: March 23, 2023
Abstract
Higher-order
networks
have
emerged
as
a
powerful
framework
to
model
complex
systems
and
their
collective
behavior.
Going
beyond
pairwise
interactions,
they
encode
structured
relations
among
arbitrary
numbers
of
units
through
representations
such
simplicial
complexes
hypergraphs.
So
far,
the
choice
between
hypergraphs
has
often
been
motivated
by
technical
convenience.
Here,
using
synchronization
an
example,
we
demonstrate
that
effects
higher-order
interactions
are
highly
representation-dependent.
In
particular,
typically
enhance
in
but
opposite
effect
complexes.
We
provide
theoretical
insight
linking
synchronizability
different
hypergraph
structures
(generalized)
degree
heterogeneity
cross-order
correlation,
which
turn
influence
wide
range
dynamical
processes
from
contagion
diffusion.
Our
findings
reveal
hidden
impact
on
dynamics,
highlighting
importance
choosing
appropriate
when
studying
with
nonpairwise
interactions.
Physical review. E,
Journal Year:
2024,
Volume and Issue:
109(1)
Published: Jan. 17, 2024
Hypergraphs
capture
the
higher-order
interactions
in
complex
systems
and
always
admit
a
factor
graph
representation,
consisting
of
bipartite
network
nodes
hyperedges.
As
hypegraphs
are
ubiquitous,
investigating
hypergraph
robustness
is
problem
major
research
interest.
In
literature
hypergraphs
so
far
only
has
been
treated
adopting
factor-graph
percolation,
which
describes
well
remain
functional
even
after
removal
one
more
their
nodes.
This
approach,
however,
fall
short
to
describe
situations
fail
when
any
removed,
this
latter
scenario
applying,
for
instance,
supply
chains,
catalytic
networks,
protein-interaction
networks
chemical
reactions,
etc.
Here
we
show
that
these
cases
correct
process
investigate
with
distinct
from
percolation.
We
build
message-passing
theory
its
critical
behavior
using
generating
function
formalism
supported
by
Monte
Carlo
simulations
on
random
real
data.
Notably,
node
percolation
threshold
exceeds
graphs.
Furthermore
differently
what
happens
ordinary
graphs,
hyperedge
do
not
coincide,
exceeding
threshold.
These
results
demonstrate
fat-tailed
cardinality
distribution
hyperedges
cannot
lead
hyper-resilience
phenomenon
contrast
where
divergent
second
moment
guarantees
zero
