Cycle-centrality in complex networks

Networks are versatile representations of the interactions between entities in complex systems. Cycles on such networks represent feedback processes which play a central role in system dynamics. In this work, we introduce a measure of the importance of any individual cycle, as the fraction of the total information flow of the network passing through the cycle. This measure is computationally cheap, numerically well-conditioned, induces a centrality measure on arbitrary subgraphs and reduces to the eigenvector centrality on vertices. We demonstrate that this measure accurately reflects the impact of events on strategic ensembles of economic sectors, notably in the US economy. As a second example, we show that in the protein-interaction network of the plant Arabidopsis thaliana, a model based on cycle-centrality better accounts for pathogen activity than the state-of-art one. This translates into pathogen-targeted-proteins being concentrated in a small number of triads with high cycle-centrality. Algorithms for computing the centrality of cycles and subgraphs are available for download

Edge centrality via the Holevo quantity

In the study of complex networks, vertex centrality measures are used to identify the most important vertices within a graph. A related problem is that of measuring the centrality of an edge. In this paper, we propose a novel edge centrality index rooted in quantum information. More specifically, we measure the importance of an edge in terms of the contribution that it gives to the Von Neumann entropy of the graph. We show that this can be computed in terms of the Holevo quantity, a well known quantum information theoretical measure. While computing the Von Neumann entropy and hence the Holevo quantity requires computing the spectrum of the graph Laplacian, we show how to obtain a simplified measure through a quadratic approximation of the Shannon entropy. This in turns shows that the proposed centrality measure is strongly correlated with the negative degree centrality on the line graph. We evaluate our centrality measure through an extensive set of experiments on real-world as well as synthetic networks, and we compare it against commonly used alternative measures

Using Network Dynamical Influence to Drive Consensus

Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing. Dynamical influence ranks the nodes with respect to their ability to influence the evolution of the associated network dynamical system. In this study it is shown that dynamical influence not only ranks the nodes, but also provides a naturally optimised distribution of effort to steer a network from one state to another. An example is provided where the "steering" refers to the physical change in velocity of self-propelled agents interacting through a network. Distinct from other works on this subject, this study looks at directed and hence more general graphs. The findings are presented with a theoretical angle, without targeting particular applications or networked systems; however, the framework and results offer parallels with biological flocks and swarms and opportunities for design of technological networks

A New Measure of Centrality for Brain Networks

Recent developments in network theory have allowed for the study of the structure and function of the human brain in terms of a network of interconnected components. Among the many nodes that form a network, some play a crucial role and are said to be central within the network structure. Central nodes may be identified via centrality metrics, with degree, betweenness, and eigenvector centrality being three of the most popular measures. Degree identifies the most connected nodes, whereas betweenness centrality identifies those located on the most traveled paths. Eigenvector centrality considers nodes connected to other high degree nodes as highly central. In the work presented here, we propose a new centrality metric called leverage centrality that considers the extent of connectivity of a node relative to the connectivity of its neighbors. The leverage centrality of a node in a network is determined by the extent to which its immediate neighbors rely on that node for information. Although similar in concept, there are essential differences between eigenvector and leverage centrality that are discussed in this manuscript. Degree, betweenness, eigenvector, and leverage centrality were compared using functional brain networks generated from healthy volunteers. Functional cartography was also used to identify neighborhood hubs (nodes with high degree within a network neighborhood). Provincial hubs provide structure within the local community, and connector hubs mediate connections between multiple communities. Leverage proved to yield information that was not captured by degree, betweenness, or eigenvector centrality and was more accurate at identifying neighborhood hubs. We propose that this metric may be able to identify critical nodes that are highly influential within the network

Controlling centrality in complex networks

Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network crucially depends on the entire pattern of connections, so that the usual approach is to compute node centralities once the network structure is assigned. We face here with the inverse problem, that is, we study how to modify the centrality scores of the nodes by acting on the structure of a given network. We show that there exist particular subsets of nodes, called controlling sets, which can assign any prescribed set of centrality values to all the nodes of a graph, by cooperatively tuning the weights of their out-going links. We found that many large networks from the real world have surprisingly small controlling sets, containing even less than 5 – 10% of the nodes

Why Do Hubs in the Yeast Protein Interaction Network Tend To Be Essential: Reexamining the Connection between the Network Topology and Essentiality

The centrality-lethality rule, which notes that high-degree nodes in a protein interaction network tend to correspond to proteins that are essential, suggests that the topological prominence of a protein in a protein interaction network may be a good predictor of its biological importance. Even though the correlation between degree and essentiality was confirmed by many independent studies, the reason for this correlation remains illusive. Several hypotheses about putative connections between essentiality of hubs and the topology of protein–protein interaction networks have been proposed, but as we demonstrate, these explanations are not supported by the properties of protein interaction networks. To identify the main topological determinant of essentiality and to provide a biological explanation for the connection between the network topology and essentiality, we performed a rigorous analysis of six variants of the genomewide protein interaction network for Saccharomyces cerevisiae obtained using different techniques. We demonstrated that the majority of hubs are essential due to their involvement in Essential Complex Biological Modules, a group of densely connected proteins with shared biological function that are enriched in essential proteins. Moreover, we rejected two previously proposed explanations for the centrality-lethality rule, one relating the essentiality of hubs to their role in the overall network connectivity and another relying on the recently published essential protein interactions model

The role of grass volatiles on oviposition site selection by Anopheles arabiensis and Anopheles coluzzii

Background: The reproductive success and population dynamics, of Anopheles malaria mosquitoes is strongly influenced by the oviposition site selection of gravid females. Mosquitoes select oviposition sites at different spatial scales, starting with selecting a habitat in which to search. This study utilizes the association of larval abundance in the field with natural breeding habitats, dominated by various types of wild grasses, as a proxy for oviposition site selection by gravid mosquitoes. Moreover, the role of olfactory cues emanating from these habitats in the attraction and oviposition stimulation of females was analysed. Methods: The density of Anopheles larvae in breeding sites associated with Echinochloa pyramidalis, Echinochloa stagnina, Typha latifolia and Cyperus papyrus, was sampled and the larvae identified to species level. Headspace volatile extracts of the grasses were collected and used to assess behavioural attraction and oviposition stimulation of gravid Anopheles arabiensis and Anopheles coluzzii mosquitoes in wind tunnel and two-choice oviposition assays, respectively. The ability of the mosquitoes to differentiate among the grass volatile extracts was tested in multi-choice tent assays. Results: Anopheles arabiensis larvae were the most abundant species found in the various grass-associated habitats. The larval densities described a hierarchical distribution, with Poaceae (Echinochloa pyramidalis and Echinochloa stagnina)-associated habitat sites demonstrating higher densities than that of Typha-associated sites, and where larvae were absent from Cyperus-associated sites. This hierarchy was maintained by gravid An. arabiensis and An. coluzzii mosquitoes in attraction, oviposition and multi-choice assays to grass volatile extracts. Conclusions: The demonstrated hierarchical preference of gravid An. coluzzii and An. arabiensis for grass volatiles indicates that vegetation cues associated with larval habitats are instrumental in the oviposition site choice of the malaria mosquitoes. Identifying volatile cues from grasses that modulate gravid malaria mosquito behaviours has distinct potential for the development of tools to be used in future monitoring and control methods