scholarly journals Higher-order temporal network effects through triplet evolution

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Qing Yao ◽  
Bingsheng Chen ◽  
Tim S. Evans ◽  
Kim Christensen
Keyword(s):  
Real World ◽  
Link Prediction ◽  
Higher Order ◽  
Prediction Algorithm ◽  
Interaction Patterns ◽  
Temporal Networks ◽  
World Systems ◽  
Order Interaction ◽  
Space And Time ◽  
Pairwise Interactions

AbstractWe study the evolution of networks through ‘triplets’—three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world data to a model based on pairwise interactions only. The significant differences between the computed matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world systems in space and time, such as our data sets. Furthermore, this also reveals that different patterns of higher-order interaction are involved in different real-world situations. To test our approach, we then use these transition matrices as the basis of a link prediction algorithm. We investigate our algorithm’s performance on four temporal networks, comparing our approach against ten other link prediction methods. Our results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as we find our method, along with two other methods based on non-local interactions, give the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems.

Link prediction based on network embedding and similarity transferring methods

2020 ◽  
Vol 34 (16) ◽  
pp. 2050169
Author(s):  
Wei Yu ◽  
Xiaoyu Liu ◽  
Bo Ouyang
Keyword(s):  
Real World ◽  
Link Prediction ◽  
Free Parameter ◽  
Network Science ◽  
Ad Hoc ◽  
Prediction Algorithm ◽  
Network Embedding ◽  
Science Community ◽  
The Cost ◽  
Accuracy Of Prediction

In network science, link prediction is a technique used to predict missing or future relationships based on currently observed connections. Much attention from the network science community is paid to this direction recently. However, most present approaches predict links based on ad hoc similarity definitions. To address this issue, we propose a link prediction algorithm named Transferring Similarity Based on Adjacency Embedding (TSBAE). TSBAE is based on network embedding, where the potential information of the structure is preserved in the embedded vector space, and the similarity is inherently captured by the distance of these vectors. Furthermore, to accommodate the fact that the similarity should be transferable, indirect similarity between nodes is incorporated to improve the accuracy of prediction. The experimental results on 10 real-world networks show that TSBAE outperforms the baseline algorithms in the task of link prediction, with the cost of tuning a free parameter in the prediction.

scholarly journals Spatio-temporal networks: reachability, centrality and robustness

2016 ◽  
Vol 3 (6) ◽  
pp. 160196 ◽  
Author(s):  
Matthew J. Williams ◽  
Mirco Musolesi
Keyword(s):  
Real World ◽  
Failure Modes ◽  
Urban Transport ◽  
Transport Systems ◽  
Centrality Measures ◽  
Complex Nature ◽  
Temporal Networks ◽  
World Systems ◽  
Temporal System ◽  
Spatio Temporal

Recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems such as urban transport networks. In this paper, we study the response of real-world spatio-temporal networks to random error and systematic attack, taking a unified view of their spatial and temporal performance. We propose a model of spatio-temporal paths in time-varying spatially embedded networks which captures the property that, as in many real-world systems, interaction between nodes is non-instantaneous and governed by the space in which they are embedded. Through numerical experiments on three real-world urban transport systems, we study the effect of node failure on a network's topological, temporal and spatial structure. We also demonstrate the broader applicability of this framework to three other classes of network. To identify weaknesses specific to the behaviour of a spatio-temporal system, we introduce centrality measures that evaluate the importance of a node as a structural bridge and its role in supporting spatio-temporally efficient flows through the network. This exposes the complex nature of fragility in a spatio-temporal system, showing that there is a variety of failure modes when a network is subject to systematic attacks.

scholarly journals Simplicial closure and higher-order link prediction

2018 ◽  
Vol 115 (48) ◽  
pp. E11221-E11230 ◽  
Author(s):  
Austin R. Benson ◽  
Rediet Abebe ◽  
Michael T. Schaub ◽  
Ali Jadbabaie ◽  
Jon Kleinberg
Keyword(s):  
Link Prediction ◽  
Higher Order ◽  
Edge Density ◽  
Limited Attention ◽  
Order Structure ◽  
Pairwise Interactions ◽  
Positive Indicators ◽  
New Interactions ◽  
Organizational Principles ◽  
Order Structures

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once—for example, communication within a group rather than person to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental difference from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.

scholarly journals Variability in higher order structure of noise added to weighted networks

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Ann S. Blevins ◽  
Jason Z. Kim ◽  
Dani S. Bassett
Keyword(s):  
Data Analysis ◽  
Real World ◽  
Higher Order ◽  
Order Structure ◽  
Complex Behavior ◽  
World Systems ◽  
Model Network ◽  
Noise Structure ◽  
Low Weight ◽  
Model Networks

AbstractThe complex behavior of many real-world systems depends on a network of both strong and weak edges. Distinguishing between true weak edges and low-weight edges caused by noise is a common problem in data analysis, and solutions tend to either remove noise or study noise in the absence of data. In this work, we instead study how noise and data coexist, by examining the structure of noisy, weak edges that have been synthetically added to model networks. We find that the structure of low-weight, noisy edges varies according to the topology of the model network to which it is added, that at least three qualitative classes of noise structure emerge, and that these noisy edges can be used to classify the model networks. Our results demonstrate that noise does not present as a monolithic nuisance, but rather as a nuanced, topology-dependent, and even useful entity in characterizing higher-order network interactions.

scholarly journals Detecting informative higher-order interactions in statistically validated hypergraphs

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Federico Musciotto ◽  
Federico Battiston ◽  
Rosario N. Mantegna
Keyword(s):  
Empirical Evidence ◽  
Real World ◽  
Open Problem ◽  
Null Hypothesis ◽  
Higher Order ◽  
Analytic Approach ◽  
Extensive Literature ◽  
World Systems

AbstractRecent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by hypergraphs, where hyperlinks encode higher-order interactions among a group of nodes. In spite of the extensive literature on networks, detecting informative hyperlinks in real world hypergraphs is still an open problem. Here we propose an analytic approach to filter hypergraphs by identifying those hyperlinks that are over-expressed with respect to a random null hypothesis, and represent the most relevant higher-order connections. We apply our method to a class of synthetic benchmarks and to several datasets, showing that the method highlights hyperlinks that are more informative than those extracted with pairwise approaches. Our method provides a first way, to the best of our knowledge, to obtain statistically validated hypergraphs, separating informative connections from noisy ones.

scholarly journals Supervised temporal link prediction in large-scale real-world networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Gerrit Jan de Bruin ◽  
Cor J. Veenman ◽  
H. Jaap van den Herik ◽  
Frank W. Takes
Keyword(s):  
Real World ◽  
Link Prediction ◽  
Large Scale ◽  
Systematic Investigation ◽  
Prediction Performance ◽  
Temporal Information ◽  
Temporal Networks ◽  
Discrete Events ◽  
New Approach ◽  
Topological Features

AbstractLink prediction is a well-studied technique for inferring the missing edges between two nodes in some static representation of a network. In modern day social networks, the timestamps associated with each link can be used to predict future links between so-far unconnected nodes. In these so-called temporal networks, we speak of temporal link prediction. This paper presents a systematic investigation of supervised temporal link prediction on 26 temporal, structurally diverse, real-world networks ranging from thousands to a million nodes and links. We analyse the relation between global structural properties of each network and the obtained temporal link prediction performance, employing a set of well-established topological features commonly used in the link prediction literature. We report on four contributions. First, using temporal information, an improvement of prediction performance is observed. Second, our experiments show that degree disassortative networks perform better in temporal link prediction than assortative networks. Third, we present a new approach to investigate the distinction between networks modelling discrete events and networks modelling persistent relations. Unlike earlier work, our approach utilises information on all past events in a systematic way, resulting in substantially higher link prediction performance. Fourth, we report on the influence of the temporal activity of the node or the edge on the link prediction performance, and show that the performance differs depending on the considered network type. In the studied information networks, temporal information on the node appears most important. The findings in this paper demonstrate how link prediction can effectively be improved in temporal networks, explicitly taking into account the type of connectivity modelled by the temporal edge. More generally, the findings contribute to a better understanding of the mechanisms behind the evolution of networks.

Phenomenological Modelling

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Real World ◽  
Biological Diversity ◽  
False Positives ◽  
World Systems ◽  
Economic Activities ◽  
Essential Services ◽  
Low Dimension ◽  
Convergent Cross Mapping

Detecting causal interactions among climatic, environmental, and human forces in complex biophysical systems is essential for understanding how these systems function and how public policies can be devised that protect the flow of essential services to biological diversity, agriculture, and other core economic activities. Convergent Cross Mapping (CCM) detects causal networks in real-world systems diagnosed with deterministic, low-dimension, and nonlinear dynamics. If CCM detects correspondence between phase spaces reconstructed from observed time series variables, then the variables are determined to causally interact in the same dynamic system. CCM can give false positives by misconstruing synchronized variables as causally interactive. Extended (delayed) CCM screens for false positives among synchronized variables.

Stable Competitive Dynamics Emerge from Multispike Interactions in a Stochastic Model of Spike-Timing-Dependent Plasticity

2006 ◽  
Vol 18 (10) ◽  
pp. 2414-2464 ◽  
Author(s):  
Peter A. Appleby ◽  
Terry Elliott
Keyword(s):  
Synaptic Plasticity ◽  
Stochastic Model ◽  
Higher Order ◽  
Spike Timing ◽  
Competitive Dynamics ◽  
Spike Timing Dependent Plasticity ◽  
Interaction Function ◽  
Dependent Plasticity ◽  
Order Interaction ◽  
Synaptic Dynamics

In earlier work we presented a stochastic model of spike-timing-dependent plasticity (STDP) in which STDP emerges only at the level of temporal or spatial synaptic ensembles. We derived the two-spike interaction function from this model and showed that it exhibits an STDP-like form. Here, we extend this work by examining the general n-spike interaction functions that may be derived from the model. A comparison between the two-spike interaction function and the higher-order interaction functions reveals profound differences. In particular, we show that the two-spike interaction function cannot support stable, competitive synaptic plasticity, such as that seen during neuronal development, without including modifications designed specifically to stabilize its behavior. In contrast, we show that all the higher-order interaction functions exhibit a fixed-point structure consistent with the presence of competitive synaptic dynamics. This difference originates in the unification of our proposed “switch” mechanism for synaptic plasticity, coupling synaptic depression and synaptic potentiation processes together. While three or more spikes are required to probe this coupling, two spikes can never do so. We conclude that this coupling is critical to the presence of competitive dynamics and that multispike interactions are therefore vital to understanding synaptic competition.

scholarly journals Asymmetry underlies stability in power grids

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ferenc Molnar ◽  
Takashi Nishikawa ◽  
Adilson E. Motter
Keyword(s):  
Symmetry Breaking ◽  
Real World ◽  
Power Grids ◽  
Stable Operation ◽  
World Systems ◽  
Symmetric State ◽  
Network Systems ◽  
Additional Improvement ◽  
The Stability ◽  
General Method

AbstractBehavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized—and thus homogeneous—across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.

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