A centrality measure for cycles and subgraphs II

In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe’s dataset and the protein-protein interaction network of the yeast Saccharomyces cerevisiae. In this latter case, we demonstrate that the centrality is able to distinguish protein complexe

The impact of partially missing communities~on the reliability of centrality measures

Network data is usually not error-free, and the absence of some nodes is a very common type of measurement error. Studies have shown that the reliability of centrality measures is severely affected by missing nodes. This paper investigates the reliability of centrality measures when missing nodes are likely to belong to the same community. We study the behavior of five commonly used centrality measures in uniform and scale-free networks in various error scenarios. We find that centrality measures are generally more reliable when missing nodes are likely to belong to the same community than in cases in which nodes are missing uniformly at random. In scale-free networks, the betweenness centrality becomes, however, less reliable when missing nodes are more likely to belong to the same community. Moreover, centrality measures in scale-free networks are more reliable in networks with stronger community structure. In contrast, we do not observe this effect for uniform networks. Our observations suggest that the impact of missing nodes on the reliability of centrality measures might not be as severe as the literature suggests

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

How to identify essential genes from molecular networks?

<p>Abstract</p> <p>Background</p> <p>The prediction of essential genes from molecular networks is a way to test the understanding of essentiality in the context of what is known about the network. However, the current knowledge on molecular network structures is incomplete yet, and consequently the strategies aimed to predict essential genes are prone to uncertain predictions. We propose that simultaneously evaluating different network structures and different algorithms representing gene essentiality (centrality measures) may identify essential genes in networks in a reliable fashion.</p> <p>Results</p> <p>By simultaneously analyzing 16 different centrality measures on 18 different reconstructed metabolic networks for <it>Saccharomyces cerevisiae</it>, we show that no single centrality measure identifies essential genes from these networks in a statistically significant way; however, the combination of at least 2 centrality measures achieves a reliable prediction of most but not all of the essential genes. No improvement is achieved in the prediction of essential genes when 3 or 4 centrality measures were combined.</p> <p>Conclusion</p> <p>The method reported here describes a reliable procedure to predict essential genes from molecular networks. Our results show that essential genes may be predicted only by combining centrality measures, revealing the complex nature of the function of essential genes.</p

A generic algorithm for layout of biological networks

BackgroundBiological networks are widely used to represent processes in biological systems and to capture interactions and dependencies between biological entities. Their size and complexity is steadily increasing due to the ongoing growth of knowledge in the life sciences. To aid understanding of biological networks several algorithms for laying out and graphically representing networks and network analysis results have been developed. However, current algorithms are specialized to particular layout styles and therefore different algorithms are required for each kind of network and/or style of layout. This increases implementation effort and means that new algorithms must be developed for new layout styles. Furthermore, additional effort is necessary to compose different layout conventions in the same diagram. Also the user cannot usually customize the placement of nodes to tailor the layout to their particular need or task and there is little support for interactive network exploration.ResultsWe present a novel algorithm to visualize different biological networks and network analysis results in meaningful ways depending on network types and analysis outcome. Our method is based on constrained graph layout and we demonstrate how it can handle the drawing conventions used in biological networks.ConclusionThe presented algorithm offers the ability to produce many of the fundamental popular drawing styles while allowing the exibility of constraints to further tailor these layouts.publishe

The pairwise disconnectivity index as a new metric for the topological analysis of regulatory networks

<p>Abstract</p> <p>Background</p> <p>Currently, there is a gap between purely theoretical studies of the topology of large bioregulatory networks and the practical traditions and interests of experimentalists. While the theoretical approaches emphasize the global characterization of regulatory systems, the practical approaches focus on the role of distinct molecules and genes in regulation. To bridge the gap between these opposite approaches, one needs to combine 'general' with 'particular' properties and translate abstract topological features of large systems into testable functional characteristics of individual components. Here, we propose a new topological parameter – the pairwise disconnectivity index of a network's element – that is capable of such bridging.</p> <p>Results</p> <p>The pairwise disconnectivity index quantifies how crucial an individual element is for sustaining the communication ability between connected pairs of vertices in a network that is displayed as a directed graph. Such an element might be a vertex (i.e., molecules, genes), an edge (i.e., reactions, interactions), as well as a group of vertices and/or edges. The index can be viewed as a measure of topological redundancy of regulatory paths which connect different parts of a given network and as a measure of sensitivity (robustness) of this network to the presence (absence) of each individual element. Accordingly, we introduce the notion of a path-degree of a vertex in terms of its corresponding incoming, outgoing and mediated paths, respectively. The pairwise disconnectivity index has been applied to the analysis of several regulatory networks from various organisms. The importance of an individual vertex or edge for the coherence of the network is determined by the particular position of the given element in the whole network.</p> <p>Conclusion</p> <p>Our approach enables to evaluate the effect of removing each element (i.e., vertex, edge, or their combinations) from a network. The greatest potential value of this approach is its ability to systematically analyze the role of every element, as well as groups of elements, in a regulatory network.</p

Using graph theory to analyze biological networks

Understanding complex systems often requires a bottom-up analysis towards a systems biology approach. The need to investigate a system, not only as individual components but as a whole, emerges. This can be done by examining the elementary constituents individually and then how these are connected. The myriad components of a system and their interactions are best characterized as networks and they are mainly represented as graphs where thousands of nodes are connected with thousands of vertices. In this article we demonstrate approaches, models and methods from the graph theory universe and we discuss ways in which they can be used to reveal hidden properties and features of a network. This network profiling combined with knowledge extraction will help us to better understand the biological significance of the system