Graph comparison via the nonbacktracking spectrum

TIBA: A web application for the visual analysis of temporal occurrences, interactions, and transitions of animal behavior

Data in behavioral research is often quantified with event-logging software, generating large data sets containing detailed information about subjects, recipients, and the duration of behaviors. Exploring and analyzing such large data sets can be challenging without tools to visualize behavioral interactions between individuals or transitions between behavioral states, yet software that can adequately visualize complex behavioral data sets is rare. TIBA (The Interactive Behavior Analyzer) is a web application for behavioral data visualization, which provides a series of interactive visualizations, including the temporal occurrences of behavioral events, the number and direction of interactions between individuals, the behavioral transitions and their respective transitional frequencies, as well as the visual and algorithmic comparison of the latter across data sets. It can therefore be applied to visualize behavior across individuals, species, or contexts. Several filtering options (selection of behaviors and individuals) together with options to set node and edge properties (in the network drawings) allow for interactive customization of the output drawings, which can also be downloaded afterwards. TIBA accepts data outputs from popular logging software and is implemented in Python and JavaScript, with all current browsers supported. The web application and usage instructions are available at tiba.inf.uni-konstanz.de. The source code is publicly available on GitHub: github.com/LSI-UniKonstanz/tiba.

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.

Network comparison and the within-ensemble graph distance

Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years, a multitude of diverse, ad hoc solutions to this problem have been introduced. Here, we propose that simple and well-understood ensembles of random networks—such as Erdős–Rényi graphs, random geometric graphs, Watts–Strogatz graphs, the configuration model and preferential attachment networks—are natural benchmarks for network comparison methods. Moreover, we show that the expected distance between two networks independently sampled from a generative model is a useful property that encapsulates many key features of that model. To illustrate our results, we calculate this within-ensemble graph distance and related quantities for classic network models (and several parameterizations thereof) using 20 distance measures commonly used to compare graphs. The within-ensemble graph distance provides a new framework for developers of graph distances to better understand their creations and for practitioners to better choose an appropriate tool for their particular task.