arXiv subjects

Fragkiskos Papadopoulos

Publications and source records attributed to Fragkiskos Papadopoulos.

At least 19 recordsLinked to original sources

arXiv2026

Temporal connection probabilities in real networks

Principled prediction of when and where links form in complex networks is a fundamental problem. We derive a closed-form non-Markovian expression for next-step connection probabilities that unifies latent hyperbolic geometry with long-range memory of past interactions. This expression yields interpretable forecasts governed by a small set of parameters. Applied to large-scale real networks, we find quantitative agreement with empirical connection probabilities and reveal how geometry and memory jointly shape link dynamics. These results establish a minimal and extensible foundation for principled probabilistic forecasting of temporal network topology.

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arXiv2024

$(\omega_1, \omega_2)$-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, $\omega_1$ and $\omega_2$. 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 $\omega_1$ and $\omega_2$ 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.

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arXiv2023

Fundamental dynamics of popularity-similarity trajectories in real networks

Real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links. Currently, there exists no principled mathematical theory for their dynamics -- a grand-challenge open problem. Here, we show that the popularity and similarity trajectories of nodes in hyperbolic embeddings of different real networks manifest universal self-similar properties with typical Hurst exponents $H \ll 0.5$. This means that the trajectories are predictable, displaying anti-persistent or 'mean-reverting' behavior, and they can be adequately captured by a fractional Brownian motion process. The observed behavior can be qualitatively reproduced in synthetic networks that possess a latent geometric space, but not in networks that lack such space, suggesting that the observed subdiffusive dynamics are inherently linked to the hidden geometry of real networks. These results set the foundations for rigorous mathematical machinery for describing and predicting real network dynamics.

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arXiv2022

Topology and Geometry of the Third-Party Domains Ecosystem: Measurement and Applications

Over the years, web content has evolved from simple text and static images hosted on a single server to a complex, interactive and multimedia-rich content hosted on different servers. As a result, a modern website during its loading time fetches content not only from its owner's domain but also from a range of third-party domains providing additional functionalities and services. Here, we infer the network of the third-party domains by observing the domains' interactions within users' browsers from all over the globe. We find that this network possesses structural properties commonly found in complex networks, such as power-law degree distribution, strong clustering, and small-world property. These properties imply that a hyperbolic geometry underlies the ecosystem's topology. We use statistical inference methods to find the domains' coordinates in this geometry, which abstract how popular and similar the domains are. The hyperbolic map we obtain is meaningful, revealing the large-scale organization of the ecosystem. Furthermore, we show that it possesses predictive power, providing us the likelihood that third-party domains are co-hosted; belong to the same legal entity; or merge under the same entity in the future in terms of company acquisition. We also find that complementarity instead of similarity is the dominant force driving future domains' merging. These results provide a new perspective on understanding the ecosystem's organization and performing related inferences and predictions.

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arXiv2022

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 $ω\in [0, 1)$. 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.

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arXiv2022

Embedding-aided network dismantling

Optimal percolation concerns the identification of the minimum-cost strategy for the destruction of any extensive connected components in a network. Solutions of such a dismantling problem are important for the design of optimal strategies of disease containment based either on immunization or social distancing. Depending on the specific variant of the problem considered, network dismantling is performed via the removal of nodes or edges, and different cost functions are associated to the removal of these microscopic elements. In this paper, we show that network representations in geometric space can be used to solve several variants of the network dismantling problem in a coherent fashion. Once a network is embedded, dismantling is implemented using intuitive geometric strategies. We demonstrate that the approach well suits both Euclidean and hyperbolic network embeddings. Our systematic analysis on synthetic and real networks demonstrates that the performance of embedding-aided techniques is comparable to, if not better than, the one of the best dismantling algorithms currently available on the market.

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arXiv2022

Dynamics of hot random hyperbolic graphs

We derive the most basic dynamical properties of random hyperbolic graphs (the distributions of contact and intercontact durations) in the hot regime (network temperature $T > 1$). We show that for sufficiently large networks the contact distribution decays as a power law with exponent $2+T > 3$ for durations $t > T$, while for $t < T$ it exhibits exponential-like decays. This result holds irrespective of the expected degree distribution, as long as it has a finite $T^{\text{th}}$ moment. Otherwise, the contact distribution depends on the expected degree distribution and we show that if the latter is a power law with exponent $γ\in (2, T+1]$, then the former decays as a power law with exponent $γ+1 > 3$. On the other hand, the intercontact distribution exhibits power-law decays with exponent $2-T \in (0, 1)$ for $T \in (1,2)$, while for $T > 2$ it displays linear decays with a slope that depends on the observation interval. This result holds irrespective of the expected degree distribution as long as it has a finite $T^{\text{th}}$ moment if $T \in (1,2)$, or a finite second moment if $T > 2$. Otherwise, the intercontact distribution depends on the expected degree distribution and if the latter is a power law with exponent $γ\in (2, 3)$, then the former decays as a power law with exponent $3-γ\in (0,1)$. Thus, hot random hyperbolic graphs can give rise to contact and intercontact distributions that both decay as power laws. These power laws however are unrealistic for the case of the intercontact distribution, as their exponent is always less than one. These results mean that hot random hyperbolic graphs are not adequate for modeling real temporal networks, in stark contrast to cold random hyperbolic graphs ($T < 1$). Since the configuration model emerges at $T \to \infty$, these results also suggest that this is not an adequate null temporal network model.

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arXiv2021

Dynamic Hidden-Variable Network Models

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many exhibit dynamics of node characteristics as well as of linking structure. Here we introduce and study natural temporal extensions of static hidden-variable network models with stochastic dynamics of hidden variables and links. The rates of the hidden variable dynamics and link dynamics are controlled by two parameters, and snapshots of networks in the dynamic models may or may not be equivalent to a static model, depending on the location in the parameter phase diagram. We quantify deviations from static-like behavior, and examine the level of structural persistence in the considered models. We explore temporal versions of popular static models with community structure, latent geometry, and degree-heterogeneity. We do not attempt to directly model real networks, but comment on interesting qualitative resemblances, discussing possible extensions, generalizations, and applications.

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arXiv2020

Hyperbolic Mapping of Human Proximity Networks

Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space. They have been extensively studied in the past 15 years as they are critical for understanding the spreading of diseases and information among humans. Here we address the problem of mapping human proximity networks into hyperbolic spaces. Each snapshot of these networks is often very sparse, consisting of a small number of interacting (i.e., non-zero degree) nodes. Yet, we show that the time-aggregated representation of such systems over sufficiently large periods can be meaningfully embedded into the hyperbolic space, using methods developed for traditional (non-mobile) complex networks. We justify this compatibility theoretically and validate it experimentally. We produce hyperbolic maps of six different real systems, and show that the maps can be used to identify communities, facilitate efficient greedy routing on the temporal network, and predict future links with significant precision. Further, we show that epidemic arrival times are positively correlated with the hyperbolic distance from the infection sources in the maps. Thus, hyperbolic embedding could also provide a new perspective for understanding and predicting the behavior of epidemic spreading in human proximity systems.

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arXiv2020

Weighted hypersoft configuration model

Maximum entropy null models of networks come in different flavors that depend on the type of constraints under which entropy is maximized. If the constraints are on degree sequences or distributions, we are dealing with configuration models. If the degree sequence is constrained exactly, the corresponding microcanonical ensemble of random graphs with a given degree sequence is the configuration model per se. If the degree sequence is constrained only on average, the corresponding grand-canonical ensemble of random graphs with a given expected degree sequence is the soft configuration model. If the degree sequence is not fixed at all but randomly drawn from a fixed distribution, the corresponding hypercanonical ensemble of random graphs with a given degree distribution is the hypersoft configuration model, a more adequate description of dynamic real-world networks in which degree sequences are never fixed but degree distributions often stay stable. Here, we introduce the hypersoft configuration model of weighted networks. The main contribution is a particular version of the model with power-law degree and strength distributions, and superlinear scaling of strengths with degrees, mimicking the properties of some real-world networks. As a byproduct, we generalize the notions of sparse graphons and their entropy to weighted networks.

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arXiv2020

k-core structure of real multiplex networks

Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous studies pointed out that real-world multiplex networks display significant inter-layer correlations -- degree-degree correlation, edge overlap, node similarities -- able to make them robust against random and targeted failures of their individual components. Here, we show that inter-layer correlations are important also in the characterization of their $\mathbf{k}$-core structure, namely the organization in shells of nodes with increasingly high degree. Understanding $k$-core structures is important in the study of spreading processes taking place on networks, as for example in the identification of influential spreaders and the emergence of localization phenomena. We find that, if the degree distribution of the network is heterogeneous, then a strong $\mathbf{k}$-core structure is well predicted by significantly positive degree-degree correlations. However, if the network degree distribution is homogeneous, then strong $\mathbf{k}$-core structure is due to positive correlations at the level of node similarities. We reach our conclusions by analyzing different real-world multiplex networks, introducing novel techniques for controlling inter-layer correlations of networks without changing their structure, and taking advantage of synthetic network models with tunable levels of inter-layer correlations.

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arXiv2019

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-$\mathbb{S}^{1}$. The dynamic-$\mathbb{S}^{1}$ does not model node mobility directly, but captures the connectivity in each snapshot---each snapshot in the model is a realization of the $\mathbb{S}^{1}$ 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, inter-contact 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-$\mathbb{S}^{1}$ 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.

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arXiv2019

Link persistence and conditional distances in multiplex networks

Recent progress towards unraveling the hidden geometric organization of real multiplexes revealed significant correlations across the hyperbolic node coordinates in different network layers, which facilitated applications like trans-layer link prediction and mutual navigation. But are geometric correlations alone sufficient to explain the topological relation between the layers of real systems? Here we provide the negative answer to this question. We show that connections in real systems tend to persist from one layer to another irrespectively of their hyperbolic distances. This suggests that in addition to purely geometric aspects the explicit link formation process in one layer impacts the topology of other layers. Based on this finding, we present a simple modification to the recently developed Geometric Multiplex Model to account for this effect, and show that the extended model can reproduce the behavior observed in real systems. We also find that link persistence is significant in all considered multiplexes and can explain their layers' high edge overlap, which cannot be explained by coordinate correlations alone. Furthermore, by taking both link persistence and hyperbolic distance correlations into account we can improve trans-layer link prediction. These findings guide the development of multiplex embedding methods, suggesting that such methods should be accounting for both coordinate correlations and link persistence across layers.

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arXiv2018

Similarity forces and recurrent components in human face-to-face interaction networks

We show that the social dynamics responsible for the formation of connected components that appear recurrently in face-to-face interaction networks, find a natural explanation in the assumption that the agents of the temporal network reside in a hidden similarity space. Distances between the agents in this space act as similarity forces directing their motion towards other agents in the physical space and determining the duration of their interactions. By contrast, if such forces are ignored in the motion of the agents recurrent components do not form, although other main properties of such networks can still be reproduced.

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arXiv2017

Geometric correlations mitigate the extreme vulnerability of multiplex networks against targeted attacks

We show that real multiplex networks are unexpectedly robust against targeted attacks on high degree nodes, and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains.

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arXiv2017

Latent geometry of bipartite networks

Despite the abundance of bipartite networked systems, their organizing principles are less studied, compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks, and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model, and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.

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arXiv2017

Hidden geometric correlations in real multiplex networks

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the individual layers. We find that these correlations are strong in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate: (i) the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers; (ii) accurate trans-layer link prediction, where connections in one layer can be predicted by observing the hidden geometric space of another layer; and (iii) efficient targeted navigation in the multilayer system using only local knowledge, which outperforms navigation in the single layers only if the geometric correlations are sufficiently strong. Our findings uncover fundamental organizing principles behind real multiplexes and can have important applications in diverse domains.

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arXiv2016

Exploiting Path Diversity in Datacenters using MPTCP-aware SDN

Recently, Multipath TCP (MPTCP) has been proposed as an alternative transport approach for datacenter networks. MPTCP provides the ability to split a flow into multiple paths thus providing better performance and resilience to failures. Usually, MPTCP is combined with flow-based Equal-Cost Multi-Path Routing (ECMP), which uses random hashing to split the MPTCP subflows over different paths. However, random hashing can be suboptimal as distinct subflows may end up using the same paths, while other available paths remain unutilized. In this paper, we explore an MPTCP-aware SDN controller that facilitates an alternative routing mechanism for the MPTCP subflows. The controller uses packet inspection to provide deterministic subflow assignment to paths. Using the controller, we show that MPTCP can deliver significantly improved performance when connections are not limited by the access links of hosts. To lessen the effect of throughput limitation due to access links, we also investigate the usage of multiple interfaces at the hosts. We demonstrate, using our modification of the MPTCP Linux Kernel, that using multiple subflows per pair of IP addresses can yield improved performance in multi-interface settings.

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