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.
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.
The Neuroscientist,
Journal Year:
2016,
Volume and Issue:
23(5), P. 499 - 516
Published: Sept. 21, 2016
It
is
nearly
20
years
since
the
concept
of
a
small-world
network
was
first
quantitatively
defined,
by
combination
high
clustering
and
short
path
length;
about
10
this
metric
complex
topology
began
to
be
widely
applied
analysis
neuroimaging
other
neuroscience
data
as
part
rapid
growth
new
field
connectomics.
Here,
we
review
briefly
foundational
concepts
graph
theoretical
estimation
generation
networks.
We
take
stock
some
key
developments
in
past
decade
consider
detail
implications
recent
studies
using
high-resolution
tract-tracing
methods
map
anatomical
networks
macaque
mouse.
In
doing
so,
draw
attention
important
methodological
distinction
between
topological
binary
or
unweighted
graphs,
which
have
provided
popular
but
simple
approach
brain
past,
weighted
retain
more
biologically
relevant
information
are
appropriate
increasingly
sophisticated
on
connectivity
emerging
from
contemporary
imaging
studies.
conclude
highlighting
possible
future
trends
further
development
small-worldness
deeper
broader
understanding
functional
value
strong
weak
links
areas
mammalian
cortex.
EPJ Data Science,
Journal Year:
2017,
Volume and Issue:
6(1)
Published: Aug. 9, 2017
Persistent
homology
(PH)
is
a
method
used
in
topological
data
analysis
(TDA)
to
study
qualitative
features
of
that
persist
across
multiple
scales.
It
robust
perturbations
input
data,
independent
dimensions
and
coordinates,
provides
compact
representation
the
input.
The
computation
PH
an
open
area
with
numerous
important
fascinating
challenges.
field
evolving
rapidly,
new
algorithms
software
implementations
are
being
updated
released
at
rapid
pace.
purposes
our
article
(1)
introduce
theory
computational
methods
for
broad
range
scientists
(2)
provide
benchmarks
state-of-the-art
PH.
We
give
friendly
introduction
PH,
navigate
pipeline
eye
towards
applications,
use
synthetic
real-world
sets
evaluate
currently
available
open-source
Based
on
benchmarking,
we
indicate
which
best
suited
different
types
sets.
In
accompanying
tutorial,
guidelines
make
publicly
all
scripts
wrote
processed
version
benchmarking.
NeuroImage,
Journal Year:
2016,
Volume and Issue:
160, P. 73 - 83
Published: Nov. 11, 2016
The
network
architecture
of
the
human
brain
has
become
a
feature
increasing
interest
to
neuroscientific
community,
largely
because
its
potential
illuminate
cognition,
variation
over
development
and
aging,
alteration
in
disease
or
injury.
Traditional
tools
approaches
study
this
have
focused
on
single
scales-of
topology,
time,
space.
Expanding
beyond
narrow
view,
we
focus
review
pertinent
questions
novel
methodological
advances
for
multi-scale
brain.
We
separate
our
exposition
into
content
related
topological
structure,
temporal
spatial
structure.
In
each
case,
recount
empirical
evidence
such
structures,
survey
network-based
reveal
these
outline
current
frontiers
open
questions.
Although
predominantly
peppered
with
examples
from
neuroimaging,
hope
that
account
will
offer
an
accessible
guide
any
neuroscientist
aiming
measure,
characterize,
understand
full
richness
brain's
multiscale
structure-irrespective
species,
imaging
modality,
resolution.
Dialogues in Clinical Neuroscience,
Journal Year:
2018,
Volume and Issue:
20(2), P. 111 - 121
Published: June 30, 2018
Network
neuroscience
is
a
thriving
and
rapidly
expanding
field.
Empirical
data
on
brain
networks,
from
molecular
to
behavioral
scales,
are
ever
increasing
in
size
complexity.
These
developments
lead
strong
demand
for
appropriate
tools
methods
that
model
analyze
network
data,
such
as
those
provided
by
graph
theory.
This
brief
review
surveys
some
of
the
most
commonly
used
neurobiologically
insightful
measures
techniques.
Among
these,
detection
communities
or
modules,
identification
central
elements
facilitate
communication
signal
transfer,
particularly
salient.
A
number
emerging
trends
growing
use
generative
models,
dynamic
(time-varying)
multilayer
well
application
algebraic
topology.
Overall,
theory
centrally
important
understanding
architecture,
development,
evolution
networks.La
neurociencia
de
la
red
es
un
campo
próspero
y
rápida
expansión.
Los
datos
empíricos
sobre
las
redes
cerebrales,
desde
niveles
moleculares
hasta
conductuales,
son
cada
vez
más
grandes
en
tamaño
complejidad.
Estos
desarrollos
llevan
una
fuerte
demanda
herramientas
métodos
apropiados
que
modelen
analicen
los
cerebral,
como
proporcionados
por
teoría
grafos.
Esta
breve
revisión
examina
algunas
medidas
técnicas
gráficas
comúnmente
empleadas
neurobiológicamente
discriminadoras.
Entre
estas,
particularmente
importantes
detección
módulos
o
comunidades
redes,
identificación
elementos
centrales
facilitan
comunicación
transferencia
señales.
Algunas
tendencias
emergentes
el
empleo
creciente
modelos
generativos,
dinámicas
(de
tiempo
variable)
multicapa,
así
aplicación
topología
algebraica.
En
general,
grafos
especialmente
para
comprender
arquitectura,
desarrollo
evolución
cerebrales.La
des
réseaux
est
domaine
florissant
qui
s'étend
rapidement.
Les
données
empiriques
sur
les
cérébraux,
l'échelle
moléculaire
à
comportementale,
ne
cessent
d'augmenter
volume
et
complexité.
Ces
développements
génèrent
une
demande
forte
d'outils
méthodes
appropriés
pour
modéliser
analyser
comme
celles
fournies
par
théorie
graphes.
Dans
cette
rapide
analyse,
nous
examinons
certaines
techniques
mesures
graphes
plus
couramment
utilisées
signifiantes
neurobiologiquement.
Parmi
elles,
détection
modules
ou
communautés
l'identification
éléments
réseau
facilite
le
transfert
du
signal,
sont
particulièrement
marquantes.
tendances
émergentes,
note
l'utilisation
croissante
modèles
génératifs,
dynamiques
(variables
avec
temps)
multi-couches,
ainsi
l'application
topologie
algébrique.
Globalement,
essentielles
comprendre
l'architecture,
développement
l'évolution
cérébraux.
Annual Review of Statistics and Its Application,
Journal Year:
2017,
Volume and Issue:
5(1), P. 501 - 532
Published: Dec. 14, 2017
Topological
data
analysis
(TDA)
can
broadly
be
described
as
a
collection
of
methods
that
find
structure
in
data.
These
include
clustering,
manifold
estimation,
nonlinear
dimension
reduction,
mode
ridge
estimation
and
persistent
homology.
This
paper
reviews
some
these
methods.
Journal of Cognitive Neuroscience,
Journal Year:
2015,
Volume and Issue:
27(8), P. 1471 - 1491
Published: March 24, 2015
Network
science
provides
theoretical,
computational,
and
empirical
tools
that
can
be
used
to
understand
the
structure
function
of
human
brain
in
novel
ways
using
simple
concepts
mathematical
representations.
neuroscience
is
a
rapidly
growing
field
providing
considerable
insight
into
structural
connectivity,
functional
connectivity
while
at
rest,
changes
networks
over
time
(dynamics),
how
these
properties
differ
clinical
populations.
In
addition,
number
studies
have
begun
quantify
network
characteristics
variety
cognitive
processes
provide
context
for
understanding
cognition
from
perspective.
this
review,
we
outline
contributions
neuroscience.
We
describe
methodology
as
applied
particular
case
neuroimaging
data
review
its
uses
investigating
range
functions
including
sensory
processing,
language,
emotion,
attention,
control,
learning,
memory.
conclusion,
discuss
current
frontiers
specific
challenges
must
overcome
integrate
complementary
disciplines
Increased
communication
between
neuroscientists
scientists
could
lead
significant
discoveries
under
an
emerging
scientific
intersection
known