Link persistence and conditional distances in multiplex networks

(ω_{1},ω_{2})-temporal random hyperbolic graphs

We extend a recent model of temporal random hyperbolic graphs by allowing connections and disconnections to persist across network snapshots with different probabilities ω_{1} and ω_{2}. This extension, while conceptually simple, poses analytical challenges involving the Appell F_{1} series. Despite these challenges, we are able to analyze key properties of the model, which include the distributions of contact and intercontact durations, as well as the expected time-aggregated degree. The incorporation of ω_{1} and ω_{2} enables more flexible tuning of the average contact and intercontact durations, and of the average time-aggregated degree, providing a finer control for exploring the effect of temporal network dynamics on dynamical processes. Overall, our results provide new insights into the analysis of temporal networks and contribute to a more general representation of real-world scenarios.

Dynamics of cold random hyperbolic graphs with link persistence

We consider and analyze a dynamic model of random hyperbolic graphs with link persistence. In the model, both connections and disconnections can be propagated from the current to the next snapshot with probability ω∈[0,1). Otherwise, with probability 1-ω, connections are reestablished according to the random hyperbolic graphs model. We show that while the persistence probability ω affects the averages of the contact and intercontact distributions, it does not affect the tails of these distributions, which decay as power laws with exponents that do not depend on ω. We also consider examples of real temporal networks, and we show that the considered model can adequately reproduce several of their dynamical properties. Our results advance our understanding of the realistic modeling of temporal networks and of the effects of link persistence on temporal network properties.

Simplicial Persistence of Financial Markets: Filtering, Generative Processes and Structural Risk

We introduce simplicial persistence, a measure of time evolution of motifs in networks obtained from correlation filtering. We observe long memory in the evolution of structures, with a two power law decay regimes in the number of persistent simplicial complexes. Null models of the underlying time series are tested to investigate properties of the generative process and its evolutional constraints. Networks are generated with both a topological embedding network filtering technique called TMFG and by thresholding, showing that the TMFG method identifies high order structures throughout the market sample, where thresholding methods fail. The decay exponents of these long memory processes are used to characterise financial markets based on their efficiency and liquidity. We find that more liquid markets tend to have a slower persistence decay. This appears to be in contrast with the common understanding that efficient markets are more random. We argue that they are indeed less predictable for what concerns the dynamics of each single variable but they are more predictable for what concerns the collective evolution of the variables. This could imply higher fragility to systemic shocks.

A Deep Learning Approach to Dynamic Interbank Network Link Prediction

Lehman Brothers’ failure in 2008 demonstrated the importance of understanding interconnectedness in interbank networks. The interbank market plays a significant role in facilitating market liquidity and providing short-term funding for each other to smooth liquidity shortages. Knowing the trading relationship could also help understand risk contagion among banks. Therefore, future lending relationship prediction is important to understand the dynamic evolution of interbank networks. To achieve the goal, we apply a deep learning framework model of interbank lending to an electronic trading interbank network for temporal trading relationship prediction. There are two important components of the model, which are the Graph convolutional network (GCN) and the Long short-term memory (LSTM) model. The GCN and LSTM components together capture the spatial–temporal information of the dynamic network snapshots. Compared with the Discrete autoregressive model and Dynamic latent space model, our proposed model achieves better performance in both the precrisis and the crisis period.

An information theoretic approach to link prediction in multiplex networks

The entities of real-world networks are connected via different types of connections (i.e., layers). The task of link prediction in multiplex networks is about finding missing connections based on both intra-layer and inter-layer correlations. Our observations confirm that in a wide range of real-world multiplex networks, from social to biological and technological, a positive correlation exists between connection probability in one layer and similarity in other layers. Accordingly, a similarity-based automatic general-purpose multiplex link prediction method-SimBins-is devised that quantifies the amount of connection uncertainty based on observed inter-layer correlations in a multiplex network. Moreover, SimBins enhances the prediction quality in the target layer by incorporating the effect of link overlap across layers. Applying SimBins to various datasets from diverse domains, our findings indicate that SimBins outperforms the compared methods (both baseline and state-of-the-art methods) in most instances when predicting links. Furthermore, it is discussed that SimBins imposes minor computational overhead to the base similarity measures making it a potentially fast method, suitable for large-scale multiplex networks.

Link prediction in real-world multiplex networks via layer reconstruction method

Networks are invaluable tools to study real biological, social and technological complex systems in which connected elements form a purposeful phenomenon. A higher resolution image of these systems shows that the connection types do not confine to one but to a variety of types. Multiplex networks encode this complexity with a set of nodes which are connected in different layers via different types of links. A large body of research on link prediction problem is devoted to finding missing links in single-layer (simplex) networks. In recent years, the problem of link prediction in multiplex networks has gained the attention of researchers from different scientific communities. Although most of these studies suggest that prediction performance can be enhanced by using the information contained in different layers of the network, the exact source of this enhancement remains obscure. Here, it is shown that similarity w.r.t. structural features (eigenvectors) is a major source of enhancements for link prediction task in multiplex networks using the proposed layer reconstruction method and experiments on real-world multiplex networks from different disciplines. Moreover, we characterize how low values of similarity w.r.t. structural features result in cases where improving prediction performance is substantially hard.

A Topological Analysis of Trade Distance: Evidence from the Gravity Model and Complex Flow Networks

As a classical trade model, the gravity model plays an important role in the trade policy-making process. However, the effect of physical distance fails to capture the effects of globalization and even ignores the multilateral resistance of trade. Here, we propose a general model describing the effective distance of trade according to multilateral trade paths information and the structure of the trade flow network. Quantifying effective trade distance aims to identify the hidden resistance information from trade networks data, and then describe trade barriers. The results show that flow distance, hybrid by multi-path constraint, and international trade network contribute to the forecasting of trade flows. Meanwhile, we also analyze the role of flow distance in international trade from two perspectives of network science and econometric model. At the econometric model level, flow distance can collapse to the predicting results of geographic distance in the proper time lagging variable, which can also reflect that flow distance contains geographical factors. At the international trade network level, community structure detection by flow distances and flow space embedding instructed that the formation of international trade networks is the tradeoff of international specialization in the trade value chain and geographical aggregation. The methodology and results can be generalized to the study of all kinds of product trade systems.

Latent geometry and dynamics of proximity networks

Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena and the performance of routing algorithms. Yet the mechanisms responsible for their observed characteristics remain elusive. Here we show that many of the observed properties of proximity networks emerge naturally and simultaneously in a simple latent space network model, called dynamic-S^{1}. The dynamic-S^{1} does not model node mobility directly but captures the connectivity in each snapshot-each snapshot in the model is a realization of the S^{1} model of traditional complex networks, which is isomorphic to hyperbolic geometric graphs. By forgoing the motion component the model facilitates mathematical analysis, allowing us to prove the contact, intercontact, and weight distributions. We show that these distributions are power laws in the thermodynamic limit with exponents lying within the ranges observed in real systems. Interestingly, we find that network temperature plays a central role in network dynamics, dictating the exponents of these distributions, the time-aggregated agent degrees, and the formation of unique and recurrent components. Further, we show that paradigmatic epidemic and rumor-spreading processes perform similarly in real and modeled networks. The dynamic-S^{1} or extensions of it may apply to other types of time-varying networks and constitute the basis of maximum likelihood estimation methods that infer the node coordinates and their evolution in the latent spaces of real systems.