15,736 research outputs found
Triadic percolation induces dynamical topological patterns in higher-order networks
Triadic interactions are higher-order interactions that occur when a set of
nodes affects the interaction between two other nodes. Examples of triadic
interactions are present in the brain when glia modulate the synaptic signals
among neuron pairs or when interneuron axon-axonic synapses enable presynaptic
inhibition and facilitation, and in ecosystems when one or more species can
affect the interaction among two other species. On random graphs, triadic
percolation has been recently shown to turn percolation into a fully-fledged
dynamical process in which the size of the giant component undergoes a route to
chaos. However, in many real cases, triadic interactions are local and occur on
spatially embedded networks. Here we show that triadic interactions in spatial
networks induce a very complex spatio-temporal modulation of the giant
component which gives rise to triadic percolation patterns with significantly
different topology. We classify the observed patterns (stripes, octopus, and
small clusters) with topological data analysis and we assess their information
content (entropy and complexity). Moreover, we illustrate the multistability of
the dynamics of the triadic percolation patterns and we provide a comprehensive
phase diagram of the model. These results open new perspectives in percolation
as they demonstrate that in presence of spatial triadic interactions, the giant
component can acquire a time-varying topology. Hence, this work provides a
theoretical framework that can be applied to model realistic scenarios in which
the giant component is time-dependent as in neuroscience.Comment: 59 pages, 11 figure
Triadic percolation induces dynamical topological patterns in higher-order networks
Triadic interactions are higher-order interactions which occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axo-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here, we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns, and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time dependent as in neuroscience
Quantifying Triadic Closure in Multi-Edge Social Networks
Multi-edge networks capture repeated interactions between individuals. In
social networks, such edges often form closed triangles, or triads. Standard
approaches to measure this triadic closure, however, fail for multi-edge
networks, because they do not consider that triads can be formed by edges of
different multiplicity. We propose a novel measure of triadic closure for
multi-edge networks of social interactions based on a shared partner statistic.
We demonstrate that our operalization is able to detect meaningful closure in
synthetic and empirical multi-edge networks, where common approaches fail. This
is a cornerstone in driving inferential network analyses from the analysis of
binary networks towards the analyses of multi-edge and weighted networks, which
offer a more realistic representation of social interactions and relations.Comment: 19 pages, 5 figures, 6 table
Triadic closure dynamics drives scaling-laws in social multiplex networks
Social networks exhibit scaling-laws for several structural characteristics,
such as the degree distribution, the scaling of the attachment kernel, and the
clustering coefficients as a function of node degree. A detailed understanding
if and how these scaling laws are inter-related is missing so far, let alone
whether they can be understood through a common, dynamical principle. We
propose a simple model for stationary network formation and show that the three
mentioned scaling relations follow as natural consequences of triadic closure.
The validity of the model is tested on multiplex data from a well studied
massive multiplayer online game. We find that the three scaling exponents
observed in the multiplex data for the friendship, communication and trading
networks can simultaneously be explained by the model. These results suggest
that triadic closure could be identified as one of the fundamental dynamical
principles in social multiplex network formation.Comment: 5 pages, 3 figure
Dynamical origins of the community structure of multi-layer societies
Social structures emerge as a result of individuals managing a variety of
different of social relationships. Societies can be represented as highly
structured dynamic multiplex networks. Here we study the dynamical origins of
the specific community structures of a large-scale social multiplex network of
a human society that interacts in a virtual world of a massive multiplayer
online game. There we find substantial differences in the community structures
of different social actions, represented by the various network layers in the
multiplex. Community size distributions are either similar to a power-law or
appear to be centered around a size of 50 individuals. To understand these
observations we propose a voter model that is built around the principle of
triadic closure. It explicitly models the co-evolution of node- and
link-dynamics across different layers of the multiplex. Depending on link- and
node fluctuation rates, the model exhibits an anomalous shattered fragmentation
transition, where one layer fragments from one large component into many small
components. The observed community size distributions are in good agreement
with the predicted fragmentation in the model. We show that the empirical
pairwise similarities of network layers, in terms of link overlap and degree
correlations, practically coincide with the model. This suggests that several
detailed features of the fragmentation in societies can be traced back to the
triadic closure processes.Comment: 8 pages, 6 figure
Triadic motifs and dyadic self-organization in the World Trade Network
In self-organizing networks, topology and dynamics coevolve in a continuous
feedback, without exogenous driving. The World Trade Network (WTN) is one of
the few empirically well documented examples of self-organizing networks: its
topology strongly depends on the GDP of world countries, which in turn depends
on the structure of trade. Therefore, understanding which are the key
topological properties of the WTN that deviate from randomness provides direct
empirical information about the structural effects of self-organization. Here,
using an analytical pattern-detection method that we have recently proposed, we
study the occurrence of triadic "motifs" (subgraphs of three vertices) in the
WTN between 1950 and 2000. We find that, unlike other properties, motifs are
not explained by only the in- and out-degree sequences. By contrast, they are
completely explained if also the numbers of reciprocal edges are taken into
account. This implies that the self-organization process underlying the
evolution of the WTN is almost completely encoded into the dyadic structure,
which strongly depends on reciprocity.Comment: 12 pages, 3 figures; Best Paper Award at the 6th International
Conference on Self-Organizing Systems, Delft, The Netherlands, 15-16/03/201
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