The Minimum Number of Hubs in Networks

In this paper, a hub refers to a non-terminal vertex of degree at least three. We study the minimum number of hubs needed in a network to guarantee certain flow demand constraints imposed between multiple pairs of sources and sinks. We prove that under the constraints, regardless of the size of the network, such minimum number is always upper bounded and we derive tight upper bounds for some special parameters. In particular, for two pairs of sources and sinks, we present a novel path-searching algorithm, the analysis of which is instrumental for the derivations of the tight upper bounds. Our results are of both theoretical and practical interest: in theory, they can be viewed as generalizations of the classical Menger’s theorem to a class of undirected graphs with multiple sources and sinks; in practice, our results, roughly speaking, suggest that for some given flow demand constraints, not “too many” hubs are needed in a network.preprin

Parameterized Complexity of Multi-Node Hubs

Hubs are high-degree nodes within a network. The examination of the emergence and centrality of hubs lies at the heart of many studies of complex networks such as telecommunication networks, biological networks, social networks and semantic networks. Furthermore, identifying and allocating hubs are routine tasks in applications. In this paper, we do not seek a hub that is a single node, but a hub that consists of k nodes. Formally, given a graph G=(V,E), we a seek a set A subseteq V of size k that induces a connected subgraph from which at least p edges emanate. Thus, we identify k nodes which can act as a unit (due to the connectivity constraint) that is a hub (due to the cut constraint). This problem, which we call Multi-Node Hub (MNH), can also be viewed as a variant of the classic Max Cut problem. While it is easy to see that MNH is W[1]-hard with respect to the parameter k, our main contribution is the first parameterized algorithm that shows that MNH is FPT with respect to the parameter p. Despite recent breakthrough advances for cut-problems like Multicut and Minimum Bisection, MNH is still very challenging. Not only does a connectivity constraint has to be handled on top of the involved machinery developed for these problems, but also the fact that MNH is a maximization problem seems to prevent the applicability of this machinery in the first place. To deal with the latter issue, we give non-trivial reduction rules that show how MNH can be preprocessed into a problem where it is necessary to delete a bounded-in-parameter number of vertices. Then, to handle the connectivity constraint, we use a novel application of the form of tree decomposition introduced by Cygan et al. [STOC 2014] to solve Minimum Bisection, where we demonstrate how connectivity constraints can be replaced by simpler size constraints. Our approach may be relevant to the design of algorithms for other cut-problems of this nature

A network approach for the scientific collaboration in the European Framework Programs

We construct the networks of collaboration between partners for projects carried out with the support of European Commission Framework Programs FP5 and FP6. We analyze in detail these networks, not only in terms of total number of projects, but also for the different tools employed, the different geographical partitions, and the different thematic areas. For all cases we find a scale free behavior, as expected for such social networks, and also reported in the literature. In comparing FP5 to FP6, we show that despite a decrease in the number of signed contracts, and the total number of unique partners, there is an increase in the average number of collaborative partners per institution. Furthermore, we establish a measure for the central role (hub) for each country, by using the Minimum Spanning Tree (MST), which we construct in detail for each thematic area (e.g. Informatics, Nanoscience, Life Sciences, etc.). The importance of these network hubs is highlighted, as this information can be used by policy planners in designing future research plans regarding the distribution of available funds.Comment: 6 pages, 4 figure

Towards a Better Understanding of the Characteristics of Fractal Networks

The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network is called fractal if the minimum number of boxes needed to cover the entire network follows a power-law relation with the size of the boxes. The fractality of networks has been associated with various network properties throughout the years, for example, disassortativity, repulsion between hubs, long-range-repulsive correlation, and small edge betweenness centralities. However, these assertions are usually based on tailor-made network models and on a small number of real networks, hence their ubiquity is often disputed. Since fractal networks have been shown to have important properties, such as robustness against intentional attacks, it is in dire need to uncover the underlying mechanisms causing fractality. Hence, the main goal of this work is to get a better understanding of the origins of fractality in complex networks. To this end, we systematically review the previous results on the relationship between various network characteristics and fractality. Moreover, we perform a comprehensive analysis of these relations on five network models and a large number of real-world networks originating from six domains. We clarify which characteristics are universally present in fractal networks and which features are just artifacts or coincidences

A Distributed Approach for Networked Flying Platform Association with Small Cells in 5G+ Networks

The densification of small-cell base stations in a 5G architecture is a promising approach to enhance the coverage area and facilitate the ever increasing capacity demand of end users. However, the bottleneck is an intelligent management of a backhaul/fronthaul network for these small-cell base stations. This involves efficient association and placement of the backhaul hubs that connects these small-cells with the core network. Terrestrial hubs suffer from an inefficient non line of sight link limitations and unavailability of a proper infrastructure in an urban area. Seeing the popularity of flying platforms, we employ here an idea of using networked flying platform (NFP) such as unmanned aerial vehicles (UAVs), drones, unmanned balloons flying at different altitudes, as aerial backhaul hubs. The association problem of these NFP-hubs and small-cell base stations is formulated considering backhaul link and NFP related limitations such as maximum number of supported links and bandwidth. Then, this paper presents an efficient and distributed solution of the designed problem, which performs a greedy search in order to maximize the sum rate of the overall network. A favorable performance is observed via a numerical comparison of our proposed method with optimal exhaustive search algorithm in terms of sum rate and run-time speed.Comment: Submitted to IEEE GLOBECOM 2017, 7 pages and 4 figure

Optimal Traffic Networks

Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a combination of topological and metric quantities. It is characterized by a strongly heterogeneous traffic, non-trivial correlations between distance and traffic and a broadly distributed centrality. A clear spatial hierarchical organization, with local hubs distributing traffic in smaller regions, emerges as a result of the optimization. Varying the parameters of the cost function, different classes of trees are recovered, including in particular the minimum spanning tree and the shortest path tree. These results suggest that a variational approach represents an alternative and possibly very meaningful path to the study of the structure of complex weighted networks.Comment: 4 pages, 4 figures, final revised versio

Cross-over behaviour in a communication network

We address the problem of message transfer in a communication network. The network consists of nodes and links, with the nodes lying on a two dimensional lattice. Each node has connections with its nearest neighbours, whereas some special nodes, which are designated as hubs, have connections to all the sites within a certain area of influence. The degree distribution for this network is bimodal in nature and has finite variance. The distribution of travel times between two sites situated at a fixed distance on this lattice shows fat fractal behaviour as a function of hub-density. If extra assortative connections are now introduced between the hubs so that each hub is connected to two or three other hubs, the distribution crosses over to power-law behaviour. Cross-over behaviour is also seen if end-to-end short cuts are introduced between hubs whose areas of influence overlap, but this is much milder in nature. In yet another information transmission process, namely, the spread of infection on the network with assortative connections, we again observed cross-over behaviour of another type, viz. from one power-law to another for the threshold values of disease transmission probability. Our results are relevant for the understanding of the role of network topology in information spread processes.Comment: 12 figure