Dimensionality of social networks using motifs and eigenvalues

We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an $m$-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when $m$ scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the distribution of motif counts, and the second exploits the eigenvalue distribution.Comment: 26 page

Noise reduction in protein-protein interaction graphs by the implementation of a novel weighting scheme

<p>Abstract</p> <p>Background</p> <p>Recent technological advances applied to biology such as yeast-two-hybrid, phage display and mass spectrometry have enabled us to create a detailed map of protein interaction networks. These interaction networks represent a rich, yet noisy, source of data that could be used to extract meaningful information, such as protein complexes. Several interaction network weighting schemes have been proposed so far in the literature in order to eliminate the noise inherent in interactome data. In this paper, we propose a novel weighting scheme and apply it to the <it>S. cerevisiae </it>interactome. Complex prediction rates are improved by up to 39%, depending on the clustering algorithm applied.</p> <p>Results</p> <p>We adopt a two step procedure. During the first step, by applying both novel and well established protein-protein interaction (PPI) weighting methods, weights are introduced to the original interactome graph based on the confidence level that a given interaction is a true-positive one. The second step applies clustering using established algorithms in the field of graph theory, as well as two variations of Spectral clustering. The clustered interactome networks are also cross-validated against the confirmed protein complexes present in the MIPS database.</p> <p>Conclusions</p> <p>The results of our experimental work demonstrate that interactome graph weighting methods clearly improve the clustering results of several clustering algorithms. Moreover, our proposed weighting scheme outperforms other approaches of PPI graph weighting.</p

An integrative approach to modeling biological networks

Networks are used to model real-world phenomena in various domains, including systems biology. Since proteins carry out biological processes by interacting with other proteins, it is expected that cellular functions are reflected in the structure of protein-protein interaction (PPI) networks. Similarly, the topology of residue interaction graphs (RIGs) that model proteins’ 3-dimensional structure might provide insights into protein folding, stability, and function. An important step towards understanding these networks is finding an adequate network model, since models can be exploited algorithmically as well as used for predicting missing data. Evaluating the fit of a model network to the data is a formidable challenge, since network comparisons are computationally infeasible and thus have to rely on heuristics, or “network properties.” We show that it is difficult to assess the reliability of the fit of a model using any network property alone. Thus, we present an integrative approach that feeds a variety of network properties into five machine learning classifiers to predict the best-fitting network model for PPI networks and RIGs. We confirm that geometric random graphs (GEO) are the best-fitting model for RIGs. Since GEO networks model spatial relationships between objects and are thus expected to replicate well the underlying structure of spatially packed residues in a protein, the good fit of GEO to RIGs validates our approach. Additionally, we apply our approach to PPI networks and confirm that the structure of merged data sets containing both binary and co-complex data that are of high coverage and confidence is also consistent with the structure of GEO, while the structure of less complete and lower confidence data is not. Since PPI data are noisy, we test the robustness of the five classifiers to noise and show that their robustness levels differ. We demonstrate that none of the classifiers predicts noisy scale-free (SF) networks as GEO, whereas noisy GEOs can be classified as SF. Thus, it is unlikely that our approach would predict a real-world network as GEO if it had a noisy SF structure. However, it could classify the data as SF if it had a noisy GEO structure. Therefore, the structure of the PPI networks is the most consistent with the structure of a noisy GEO