Ensembles based on the Rich-Club and how to use them to build soft-communities

16 pages, 5 figures16 pages, 5 figures16 pages, 5 figuresEnsembles of networks are used as null-models to discriminate network structures. We present an efficient algorithm, based on the maximal entropy method to generate network ensembles defined by the degree sequence and the rich-club coefficient. The method is applicable for unweighted, undirected networks. The ensembles are used to generate correlated and uncorrelated null--models of a real networks. These ensembles can be used to define the partition of a network into soft communities

Beyond the rich-club: Properties of networks related to the better connected nodes

35 pages, 16 figures35 pages, 16 figuresMany of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In here we revise and present new results showing how to construct network ensembles which give a good approximation to the degree-degree correlations, and hence to the projections of this correlation like the assortativity coefficient or the average neighbours degree. We present a new bound for the structural cut--off degree based on the connectivity within the hubs. Also we show that the connections with and within the hubs can be used to define different networks cores. Two of these cores are related to the spectral properties and walks of length one and two which contain at least on hub node, and they are related to the eigenvector centrality. We introduce a new centrality measured based on the connectivity with the hubs. In addition, as the ensembles and cores are related by the connectivity of the hubs, we show several examples how changes in the hubs linkage effects the degree--degree correlations and core properties

The missing links in the BGP-based AS connectivity maps

PAM2003 - The Passive and Active Measurement Workshop(http://www.pam2003.org), San Diego, USA, April 2003PAM2003 - The Passive and Active Measurement Workshop(http://www.pam2003.org), San Diego, USA, April 2003PAM2003 - The Passive and Active Measurement Workshop(http://www.pam2003.org), San Diego, USA, April 2003A number of recent studies of the Internet topology at the autonomous systems level (AS graph) are based on the BGP-based AS connectivity maps (original maps). The so-called extended maps use additional data sources and contain more complete pictures of the AS graph. In this paper, we compare an original map, an extended map and a synthetic map generated by the Barabasi-Albert model. We examine the recently reported rich-club phenomenon, alternative routing paths and attack tolerance. We point out that the majority of the missing links of the original maps are the connecting links between rich nodes (nodes with large numbers of links) of the extended maps. We show that the missing links are relevant because links between rich nodes can be crucial for the network structure

Ensembles related to the rich-club coefficient for non-evolving networks

15 pages, 7 figures15 pages, 7 figures15 pages, 7 figuresIn complex networks the rich nodes are the subset of nodes with high degree. These well connected nodes tend to dominate the organisation of the network's structure. In non-evolving networks, a reference network has been used to detect if the connectivity between the rich nodes is due to chance or caused by an unknown mechanism. Chance is represented as a reference network obtained from an ensemble of networks. When compared with the original network the reference network discounts suggests the existence of a well connected rich club beyond structural constraints. Here we revise some of the properties of the ensemble obtained by conserving only the degree distribution and introduce two new reference networks to study the importance of the rich nodes as organisers of the network structure. The first reference network is obtained from an ensemble of networks where all the members of the ensemble have the same rich--club coefficient. The reference network obtained from the ensemble is assortative. We propose that this reference network can be used to study networks where assortativness is a fundamental property, a common case in many social networks. The second reference network is obtained from an ensemble where the members of the ensemble all have the same probability degree distribution and rich-club coefficient. The reference network obtained from this ensemble has a very similar structure to the original network. This ensemble can be used to quantify correlations between the rich nodes and pinpoint which links are the backbone of the network's structure

Rich-Cores in Networks

A core is said to be a group of central and densely connected nodes which governs the overall behavior of a network. Profiling this meso--scale structure currently relies on a limited number of methods which are often complex, and have scalability issues when dealing with very large networks. As a result, we are yet to fully understand its impact on network properties and dynamics. Here we introduce a simple method to profile this structure by combining the concepts of core/periphery and rich-club. The key challenge in addressing such association of the two concepts is to establish a way to define the membership of the core. The notion of a "rich-club" describes nodes which are essentially the hub of a network, as they play a dominating role in structural and functional properties. Interestingly, the definition of a rich-club naturally emphasizes high degree nodes and divides a network into two subgroups. Our approach theoretically couples the underlying principle of a rich-club with the escape time of a random walker, and a rich-core is defined by examining changes in the associated persistence probability. The method is fast and scalable to large networks. In particular, we successfully show that the evolution of the core in \emph{C. elegans} and World Trade networks correspond to key development stages and responses to historical events respectively.Comment: 12 pages, 6 figure

Weighted Multiplex Networks

One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex nature. Multiplex networks are multilayer systems of $N$ nodes that can be linked in multiple interacting and co-evolving layers. In these networks, relevant information might not be captured if the single layers were analyzed separately. Here we demonstrate that such partial analysis of layers fails to capture significant correlations between weights and topology of complex multiplex networks. To this end, we study two weighted multiplex co-authorship and citation networks involving the authors included in the American Physical Society. We show that in these networks weights are strongly correlated with multiplex structure, and provide empirical evidence in favor of the advantage of studying weighted measures of multiplex networks, such as multistrength and the inverse multiparticipation ratio. Finally, we introduce a theoretical framework based on the entropy of multiplex ensembles to quantify the information stored in multiplex networks that would remain undetected if the single layers were analyzed in isolation.Comment: (22 pages, 10 figures

Extraction of topological features from communication network topological patterns using self-organizing feature maps

8 Pages, 5 figures, To be appeared in IEE Electronics Letter Journal8 Pages, 5 figures, To be appeared in IEE Electronics Letter Journal8 Pages, 5 figures, To be appeared in IEE Electronics Letter JournalDifferent classes of communication network topologies and their representation in the form of adjacency matrix and its eigenvalues are presented. A self-organizing feature map neural network is used to map different classes of communication network topological patterns. The neural network simulation results are reported

Funding shapes the anatomy of scientific research

Main text: 10 pages with 4 figuresMain text: 10 pages with 4 figuresResearch projects are primarily collaborative in nature through internal and external partnerships, but what role does funding play in their formation? Here, we examined over 43,000 funded projects in the past three decades, enabling us to characterise changes in the funding landscape and their impacts on the underlying collaboration patterns. We observed rising inequality in the distribution of funding and its effect was most noticeable at the institutional level in which the leading universities diversified their collaborations and increasingly became the knowledge brokers. Furthermore, these universities formed a cohesive core through their close ties, and such reliance appeared to be a key for their research success, with the elites in the core over-attracting resources but in turn rewarding in both research breadth and depth. Our results reveal how collaboration networks undergo previously unknown adaptive organisation in response to external driving forces, which can have far-reaching implications for future policy

Antibody response to sand fly saliva is a marker of transmission intensity but not disease progression in dogs naturally infected with Leishmania infantum

BACKGROUND: Antibody responses to sand fly saliva have been suggested to be a useful marker of exposure to sand fly bites and Leishmania infection and a potential tool to monitor the effectiveness of entomological interventions. Exposure to sand fly bites before infection has also been suggested to modulate the severity of the infection. Here, we test these hypotheses by quantifying the anti-saliva IgG response in a cohort study of dogs exposed to natural infection with Leishmania infantum in Brazil. METHODS: IgG responses to crude salivary antigens of the sand fly Lutzomyia longipalpis were measured by ELISA in longitudinal serum samples from 47 previously unexposed sentinel dogs and 11 initially uninfected resident dogs for up to 2 years. Antibody responses were compared to the intensity of transmission, assessed by variation in the incidence of infection between seasons and between dogs. Antibody responses before patent infection were then compared with the severity of infection, assessed using tissue parasite loads and clinical symptoms. RESULTS: Previously unexposed dogs acquired anti-saliva antibody responses within 2 months, and the rate of acquisition increased with the intensity of seasonal transmission. Over the following 2 years, antibody responses varied with seasonal transmission and sand fly numbers, declining rapidly in periods of low transmission. Antibody responses varied greatly between dogs and correlated with the intensity of transmission experienced by individual dogs, measured by the number of days in the field before patent infection. After infection, anti-saliva antibody responses were positively correlated with anti-parasite antibody responses. However, there was no evidence that the degree of exposure to sand fly bites before infection affected the severity of the infection. CONCLUSIONS: Anti-saliva antibody responses are a marker of current transmission intensity in dogs exposed to natural infection with Leishmania infantum, but are not associated with the outcome of infection