Navigability of temporal networks in hyperbolic space

Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remain largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We find that such dynamics enhances navigability with respect to the static case. Interestingly, there exists an optimal intermediate activation value, which ensures the best trade-off between the increase in the number of successful paths and a limited growth of their length. Contrary to expectations, the enhanced navigability is robust even when the most connected nodes inactivate with very high probability. Finally, our results indicate that some real networks are ultranavigable and remain highly navigable even if the network structure is extremely unsteady. These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.Comment: 10 pages, 4 figures. Includes Supplemental Informatio

Navigability of temporal networks in hyperbolic space

Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remains largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We find that such dynamics enhances navigability with respect to the static case. Interestingly, there exists an optimal intermediate activation value, which ensures the best trade-off between the increase in the number of successful paths and a limited growth of their length. Contrary to expectations, the enhanced navigability is robust even when the most connected nodes inactivate with very high probability. Finally, our results indicate that some real networks are ultranavigable and remain highly navigable even if the network structure is extremely unsteady. These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks

Greedy Navigational Cores in the Human Brain

Greedy navigation/routing plays an important role in geometric routing of networks because of its locality and simplicity. This can operate in geometrically embedded networks in a distributed manner, distances are calculated based on coordinates of network nodes for choosing the next hop in the routing. Based only on node coordinates in any metric space, the Greedy Navigational Core (GNC) can be identified as the minimum set of links between these nodes which provides 100% greedy navigability. In this paper we perform results on structural greedy navigability as the level of presence of Greedy Navigational Cores in structural networks of the Human Brain

Latent Geometry Inspired Graph Dissimilarities Enhance Affinity Propagation Community Detection in Complex Networks

Affinity propagation is one of the most effective unsupervised pattern recognition algorithms for data clustering in high-dimensional feature space. However, the numerous attempts to test its performance for community detection in complex networks have been attaining results very far from the state of the art methods such as Infomap and Louvain. Yet, all these studies agreed that the crucial problem is to convert the unweighted network topology in a 'smart-enough' node dissimilarity matrix that is able to properly address the message passing procedure behind affinity propagation clustering. Here we introduce a conceptual innovation and we discuss how to leverage network latent geometry notions in order to design dissimilarity matrices for affinity propagation community detection. Our results demonstrate that the latent geometry inspired dissimilarity measures we design bring affinity propagation to equal or outperform current state of the art methods for community detection. These findings are solidly proven considering both synthetic 'realistic' networks (with known ground-truth communities) and real networks (with community metadata), even when the data structure is corrupted by noise artificially induced by missing or spurious connectivity

Scale-free networks and scalable interdomain routing

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia InformáticaThe exponential growth of the Internet, due to its tremendous success, has brought to light some limitations of the current design at the routing and arquitectural level, such as scalability and convergence as well as the lack of support for traffic engineering, mobility, route differentiation and security. Some of these issues arise from the design of the current architecture, while others are caused by the interdomain routing scheme - BGP. Since it would be quite difficult to add support for the aforementioned issues, both in the interdomain architecture and in the in the routing scheme, various researchers believe that a solution can only achieved via a new architecture and (possibly) a new routing scheme. A new routing strategy has emerged from the studies regarding large-scale networks, which is suitable for a special type of large-scale networks which characteristics are independent of network size: scale-free networks. Using the greedy routing strategy a node routes a message to a given destination using only the information regarding the destination and its neighbours, choosing the one which is closest to the destination. This routing strategy ensures the following remarkable properties: routing state in the order of the number of neighbours; no requirements on nodes to exchange messages in order to perform routing; chosen paths are the shortest ones. This dissertation aims at: studying the aforementioned problems, studying the Internet configuration as a scale-free network, and defining a preliminary path onto the definition of a greedy routing scheme for interdomain routing

Navigability and synchronization in complex networks: a computational approach

Les xarxes complexes han demostrat ser una eina molt valuosa per estudiar sistemes reals, en part, gràcies a la creixent capacitat de computació. En aquesta tesi abordem computacionalment diversos problemes dividits en dos blocs. El primer bloc està motivat pels problemes que planteja la ràpida evolució de la Internet. D’una banda, el creixement exponencial de la xarxa està comprometent la seva escalabilitat per les dependències a les taules d’enrutament globals. Al Capítol 4 proposem un esquema d’enrutament descentralitzat que fa servir la projecció TSVD de l’estructura mesoscòpica de la xarxa com a mapa. Els resultats mostren que fent servir informació local podem guiar amb èxit en l’enrutament. Al Capítol 3 també avaluem la fiabilitat d’aquesta projecció davant el creixement de la xarxa. Els resultats indiquen que aquest mapa és robust i no necessita actualitzacions contínues. D’altra banda, la creixent demanda d’ample de banda és un factor potencial per produir congestió. Al Capítol 5 estenem un esquema d’enrutament dinàmic en el context de les xarxes multiplex, i l’analitzem amb xarxes sintètiques amb diferents assortativitats d’acoblament. Els resultats mostren que tenir en compte el volum de trànsit en l’enrutament retarda l’inici de la congestió. Tot i això, la distribució uniforme del trànsit produeix una transició de fase abrupta. Amb tot, l’acoblament assortatiu es presenta com la millor opció per a dissenys de xarxes òptimes. El segon bloc ve motivat per l’actual crisi financera mundial. Al Capítol 6 proposem estudiar la propagació de les crisis econòmiques utilitzant un model simple de xarxa formada per oscil·ladors integrate-and-fire, i caracteritzar la seva sincronització durant l’evolució de la xarxa de comerç. Els resultats mostren l’aparició d’un procés de globalització que dilueix les fronteres topològiques i accelera la propagació de les crisis financeres.Las redes complejas han demostrado ser una herramienta muy valiosa para estudiar sistemas reales, en parte, gracias a la creciente capacidad de computación. En esta tesis abordamos computacionalmente varios problemas divididos en dos bloques. El primer bloque está motivado por los problemas que plantea la rápida evolución de Internet. Por un lado, el crecimiento exponencial de la red está comprometiendo su escalabilidad por las dependencias a las tablas de enrutado globales. En el Capítulo 4 proponemos un esquema de enrutamiento descentralizado que utiliza la proyección TSVD de la estructura mesoscópica de la red como mapa. Los resultados muestran que utilizando información local podemos guiar con éxito el enrutado. En el Calítulo 3 también evaluamos la fiabilidad de esta proyección bajo cambios en la topología de la red. Los resultados indican que este mapa es robusto y no necesita actualizaciones continuas. Por otra parte, la creciente demanda de ancho de banda es un factor potencial de congestión. En el Capítulo 5 extendemos un esquema de enrutamiento dinámico en el marco de las redes multiplex, y lo analizamos en redes sintéticas con distintas asortatividades de acoplamiento. Los resultados muestran que tener en cuenta el volumen de tráfico en el enrutado retrasa la congestión. Sin embargo, la distribución uniforme del tráfico produce una transición de fase abrupta. Además, el acoplamiento asortativo se presenta como la mejor opción para diseños de redes óptimas. El segundo bloque viene motivado por la actual crisis financiera mundial. En el Capítulo 6 proponemos estudiar la propagación de las crisis económicas utilizando un modelo simple de red formada por osciladores integrate-and-fire, y caracterizar su sincronización durante la evolución de la red de comercio. Los resultados muestran la aparición de un proceso de globalización que diluye las fronteras topológicas y acelera la propagación de las crisis financieras.Complex networks are a powerful tool to study many real systems, partly thanks to the increasing capacity of computational resources. In this dissertation we address computationally a broad scope of problems that are framed in two parts. The first part is motivated by the issues posed by the rapid evolution of the Internet. On one side, the exponential growth of the network is compromising its scalability due to dependencies on global routing tables. In Chapter 4 we propose a decentralized routing scheme that exploits the TSVD projection of the mesoscopic structure of the network as a map. The results show that, using only local information, we can achieve good success rates in the routing process. Additionally, Chapter 3 evaluates the reliability of this projection when network topology changes. The results indicate that this map is very robust and does not need continual updates. On the other side, the increasing bandwidth demand is a potential trigger for congestion episodes. In Chapter 5 we extend a dynamic traffic-aware routing scheme to the context of multiplex networks, and we conduct the analysis on synthetic networks with different coupling assortativity. The results show that considering the traffic load in the transmission process delays the congestion onset. However, the uniform distribution of traffic produces an abrupt phase transition from free-flow to congested state. Withal, assortative coupling is depicted as the best consideration for optimal network designs. The second part is motivated by the current global financial crises. Chapter 6 presents a study on the spreading of economic crises using a simple model of networked integrate-and-fire oscillators and we characterize synchronization process on the evolving trade network. The results show the emergence of a globalization process that dilutes the topological borders and accelerates the spreading of financial crashes