2,832 research outputs found

    Metrics for Graph Comparison: A Practitioner's Guide

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    Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as λ\lambda distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work

    Local versus Global Knowledge in the Barabasi-Albert scale-free network model

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    The scale-free model of Barabasi and Albert gave rise to a burst of activity in the field of complex networks. In this paper, we revisit one of the main assumptions of the model, the preferential attachment rule. We study a model in which the PA rule is applied to a neighborhood of newly created nodes and thus no global knowledge of the network is assumed. We numerically show that global properties of the BA model such as the connectivity distribution and the average shortest path length are quite robust when there is some degree of local knowledge. In contrast, other properties such as the clustering coefficient and degree-degree correlations differ and approach the values measured for real-world networks.Comment: Revtex format. Final version appeared in PR

    Hierarchy and assortativity as new tools for affinity investigation: the case of the TBA aptamer-ligand complex

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    Aptamers are single stranded DNA, RNA or peptide sequences having the ability to bind a variety of specific targets (proteins, molecules as well as ions). Therefore, aptamer production and selection for therapeutic and diagnostic applications is very challenging. Usually they are in vitro generated, but, recently, computational approaches have been developed for the in silico selection, with a higher affinity for the specific target. Anyway, the mechanism of aptamer-ligand formation is not completely clear, and not obvious to predict. This paper aims to develop a computational model able to describe aptamer-ligand affinity performance by using the topological structure of the corresponding graphs, assessed by means of numerical tools such as the conventional degree distribution, but also the rank-degree distribution (hierarchy) and the node assortativity. Calculations are applied to the thrombin binding aptamer (TBA), and the TBA-thrombin complex, produced in the presence of Na+ or K+. The topological analysis reveals different affinity performances between the macromolecules in the presence of the two cations, as expected by previous investigations in literature. These results nominate the graph topological analysis as a novel theoretical tool for testing affinity. Otherwise, starting from the graphs, an electrical network can be obtained by using the specific electrical properties of amino acids and nucleobases. Therefore, a further analysis concerns with the electrical response, which reveals that the resistance sensitively depends on the presence of sodium or potassium thus posing resistance as a crucial physical parameter for testing affinity.Comment: 12 pages, 5 figure

    Multiplicative Attribute Graph Model of Real-World Networks

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    Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and especially in social networks, nodes have a rich set of attributes (e.g., age, gender) associated with them. Here we present a model that we refer to as the Multiplicative Attribute Graphs (MAG), which naturally captures the interactions between the network structure and the node attributes. We consider a model where each node has a vector of categorical latent attributes associated with it. The probability of an edge between a pair of nodes then depends on the product of individual attribute-attribute affinities. The model yields itself to mathematical analysis and we derive thresholds for the connectivity and the emergence of the giant connected component, and show that the model gives rise to networks with a constant diameter. We analyze the degree distribution to show that MAG model can produce networks with either log-normal or power-law degree distributions depending on certain conditions.Comment: 33 pages, 6 figure

    Probing the Extent of Randomness in Protein Interaction Networks

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    Protein–protein interaction (PPI) networks are commonly explored for the identification of distinctive biological traits, such as pathways, modules, and functional motifs. In this respect, understanding the underlying network structure is vital to assess the significance of any discovered features. We recently demonstrated that PPI networks show degree-weighted behavior, whereby the probability of interaction between two proteins is generally proportional to the product of their numbers of interacting partners or degrees. It was surmised that degree-weighted behavior is a characteristic of randomness. We expand upon these findings by developing a random, degree-weighted, network model and show that eight PPI networks determined from single high-throughput (HT) experiments have global and local properties that are consistent with this model. The apparent random connectivity in HT PPI networks is counter-intuitive with respect to their observed degree distributions; however, we resolve this discrepancy by introducing a non-network-based model for the evolution of protein degrees or “binding affinities.” This mechanism is based on duplication and random mutation, for which the degree distribution converges to a steady state that is identical to one obtained by averaging over the eight HT PPI networks. The results imply that the degrees and connectivities incorporated in HT PPI networks are characteristic of unbiased interactions between proteins that have varying individual binding affinities. These findings corroborate the observation that curated and high-confidence PPI networks are distinct from HT PPI networks and not consistent with a random connectivity. These results provide an avenue to discern indiscriminate organizations in biological networks and suggest caution in the analysis of curated and high-confidence networks

    A simple physical model for scaling in protein-protein interaction networks

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    It has recently been demonstrated that many biological networks exhibit a scale-free topology where the probability of observing a node with a certain number of edges (k) follows a power law: i.e. p(k) ~ k^-g. This observation has been reproduced by evolutionary models. Here we consider the network of protein-protein interactions and demonstrate that two published independent measurements of these interactions produce graphs that are only weakly correlated with one another despite their strikingly similar topology. We then propose a physical model based on the fundamental principle that (de)solvation is a major physical factor in protein-protein interactions. This model reproduces not only the scale-free nature of such graphs but also a number of higher-order correlations in these networks. A key support of the model is provided by the discovery of a significant correlation between number of interactions made by a protein and the fraction of hydrophobic residues on its surface. The model presented in this paper represents the first physical model for experimentally determined protein-protein interactions that comprehensively reproduces the topological features of interaction networks. These results have profound implications for understanding not only protein-protein interactions but also other types of scale-free networks.Comment: 50 pages, 17 figure
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