Models of similarity in complex networks

The analysis of networks describing many social, economic, technological, biological and other systems has attracted a lot of attention last decades. Since most of these complex systems evolve over time, there is a need to investigate the changes, which appear in the system, in order to assess the sustainability of the network and to identify stable periods. In the literature, there have been developed a large number of models that measure the similarity among the networks. There also exist some surveys, which consider a limited number of similarity measures and then perform their correlation analysis, discuss their properties or assess their performances on synthetic benchmarks or real networks. The aim of the article is to extend these studies. The article considers 39 graph distance measures and compares them on simple graphs, random graph models and real networks. The author also evaluates the performance of the models in order to identify which of them can be applied to large networks. The results of the study reveal some important aspects of existing similarity models and provide a better understanding of their advantages and disadvantages. The major finding of the work is that many graph similarity measures of different nature are well correlated and that some comprehensive methods are well agreed with simple models. Such information can be used for the choice of appropriate similarity measure as well as for further development of new models for similarity assessment in network structures.

Brain network similarity: methods and applications

Graph theoretical approach has proved an effective tool to understand, characterize, and quantify the complex brain network. However, much less attention has been paid to methods that quantitatively compare two graphs, a crucial issue in the context of brain networks. Comparing brain networks is indeed mandatory in several network neuroscience applications. Here, we discuss the current state of the art, challenges, and a collection of analysis tools that have been developed in recent years to compare brain networks. We first introduce the graph similarity problem in brain network application. We then describe the methodological background of the available metrics and algorithms of comparing graphs, their strengths, and limitations. We also report results obtained in concrete applications from normal brain networks. More precisely, we show the potential use of brain network similarity to build a “network of networks” that may give new insights into the object categorization in the human brain. Additionally, we discuss future directions in terms of network similarity methods and applications.

Multilayer network based comparative document analysis (MUNCoDA)

The proposed multilayer network-based comparative document analysis (MUNCoDA) method supports the identification of the common points of a set of documents, which deal with the same subject area. As documents are transformed into networks of informative word-pairs, the collection of documents form a multilayer network that allows the comparative evaluation of the texts. The multilayer network can be visualized and analyzed to highlight how the texts are structured. The topics of the documents can be clustered based on the developed similarity measures. By exploring the network centralities, topic importance values can be assigned. The method is fully automated by KNIME preprocessing tools and MATLAB/Octave code.•Networks can be formed based on informative word pairs of a multiple documents•The analysis of the proposed multilayer networks provides information for multi-document summarization•Words and documents can be clustered based on node similarity and edge overlap measures.

Intersubject similarity of personality is associated with intersubject similarity of brain connectivity patterns

Personality is a central high-level psychological concept that defines individual human beings and has been associated with a variety of real-world outcomes (e.g., mental health and academic performance). Using 2 h, high resolution, functional magnetic resonance imaging (fMRI) resting state data of 984 (primary dataset N = 801, hold-out dataset N = 183) participants from the Human Connectome Project (HCP), we investigated the relationship between personality (five-factor model, FFM) and intrinsic whole-brain functional connectome. We found a pattern of functional brain connectivity ("global personality network") related to personality traits. Consistent with the heritability of personality traits, the connectivity strength of this global personality network is also heritable (more similar between monozygotic twin pairs compared to the dizygotic twin pairs). Validated by both the repeated family-based 10-fold cross-validation and hold-out dataset, our intersubject network similarity analysis allowed us to identify participants' pairs with similar personality profiles. Across all the identified pairs of participants, we found a positive correlation between the network similarity and personality similarity, supporting our "similar brain, similar personality" hypothesis. Furthermore, the global personality network can be used to predict the individual subject's responses in the personality questionnaire on an item level. In sum, based on individual brain connectivity pattern, we could predict different facets of personality, and this prediction is not based on localized regions, but rather relies on the individual connectivity pattern in large-scale brain networks.

Identification of common coexpression modules based on quantitative network comparison

Background

Finding common molecular interactions from different samples is essential work to understanding diseases and other biological processes. Coexpression networks and their modules directly reflect sample-specific interactions among genes. Therefore, identification of common coexpression network or modules may reveal the molecular mechanism of complex disease or the relationship between biological processes. However, there has been no quantitative network comparison method for coexpression networks and we examined previous methods for other networks that cannot be applied to coexpression network. Therefore, we aimed to propose quantitative comparison methods for coexpression networks and to find common biological mechanisms between Huntington’s disease and brain aging by the new method.

Results

We proposed two similarity measures for quantitative comparison of coexpression networks. Then, we performed experiments using known coexpression networks. We showed the validity of two measures and evaluated threshold values for similar coexpression network pairs from experiments. Using these similarity measures and thresholds, we quantitatively measured the similarity between disease-specific and aging-related coexpression modules and found similar Huntington’s disease-aging coexpression module pairs.

Conclusions

We identified similar Huntington’s disease-aging coexpression module pairs and found that these modules are related to brain development, cell death, and immune response. It suggests that up-regulated cell signalling related cell death and immune/ inflammation response may be the common molecular mechanisms in the pathophysiology of HD and normal brain aging in the frontal cortex.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2193-3) contains supplementary material, which is available to authorized users.

Fair evaluation of global network aligners

BACKGROUND

Analogous to genomic sequence alignment, biological network alignment identifies conserved regions between networks of different species. Then, function can be transferred from well- to poorly-annotated species between aligned network regions. Network alignment typically encompasses two algorithmic components: node cost function (NCF), which measures similarities between nodes in different networks, and alignment strategy (AS), which uses these similarities to rapidly identify high-scoring alignments. Different methods use both different NCFs and different ASs. Thus, it is unclear whether the superiority of a method comes from its NCF, its AS, or both. We already showed on state-of-the-art methods, MI-GRAAL and IsoRankN, that combining NCF of one method and AS of another method can give a new superior method. Here, we evaluate MI-GRAAL against a newer approach, GHOST, by mixing-and-matching the methods' NCFs and ASs to potentially further improve alignment quality. While doing so, we approach important questions that have not been asked systematically thus far. First, we ask how much of the NCF information should come from protein sequence data compared to network topology data. Existing methods determine this parameter more-less arbitrarily, which could affect alignment quality. Second, when topological information is used in NCF, we ask how large the size of the neighborhoods of the compared nodes should be. Existing methods assume that the larger the neighborhood size, the better.

RESULTS

Our findings are as follows. MI-GRAAL's NCF is superior to GHOST's NCF, while the performance of the methods' ASs is data-dependent. Thus, for data on which GHOST's AS is superior to MI-GRAAL's AS, the combination of MI-GRAAL's NCF and GHOST's AS represents a new superior method. Also, which amount of sequence information is used within NCF does not affect alignment quality, while the inclusion of topological information is crucial for producing good alignments. Finally, larger neighborhood sizes are preferred, but often, it is the second largest size that is superior. Using this size instead of the largest one would decrease computational complexity.

CONCLUSION

Taken together, our results represent general recommendations for a fair evaluation of network alignment methods and in particular of two-stage NCF-AS approaches.