Community Structure Characterization

This entry discusses the problem of describing some communities identified in a complex network of interest, in a way allowing to interpret them. We suppose the community structure has already been detected through one of the many methods proposed in the literature. The question is then to know how to extract valuable information from this first result, in order to allow human interpretation. This requires subsequent processing, which we describe in the rest of this entry

Characterizing time series : when Granger causality triggers complex networks

In this paper, we propose a new approach to characterize time series with noise perturbations in both the time and frequency domains by combining Granger causality and complex networks. We construct directed and weighted complex networks from time series and use representative network measures to describe their physical and topological properties. Through analyzing the typical dynamical behaviors of some physical models and the MIT-BIH* human electrocardiogram data sets, we show that the proposed approach is able to capture and characterize various dynamics and has much potential for analyzing real-world time series of rather short length

Multilayer Complex Network Descriptors for Color-Texture Characterization

A new method based on complex networks is proposed for color-texture analysis. The proposal consists on modeling the image as a multilayer complex network where each color channel is a layer, and each pixel (in each color channel) is represented as a network vertex. The network dynamic evolution is accessed using a set of modeling parameters (radii and thresholds), and new characterization techniques are introduced to capt information regarding within and between color channel spatial interaction. An automatic and adaptive approach for threshold selection is also proposed. We conduct classification experiments on 5 well-known datasets: Vistex, Usptex, Outex13, CURet and MBT. Results among various literature methods are compared, including deep convolutional neural networks with pre-trained architectures. The proposed method presented the highest overall performance over the 5 datasets, with 97.7 of mean accuracy against 97.0 achieved by the ResNet convolutional neural network with 50 layers.Comment: 20 pages, 7 figures and 4 table

Hierarchical Features of Large-Scale Cortical Connectivity

The analysis of complex networks has revealed patterns of organization in a variety of natural and artificial systems, including neuronal networks of the brain at multiple scales. In this paper, we describe a novel analysis of the large-scale connectivity between regions of the mammalian cerebral cortex, utilizing a set of hierarchical measurements proposed recently. We examine previously identified functional clusters of brain regions in macaque visual cortex and cat cortex and find significant differences between such clusters in terms of several hierarchical measures, revealing differences in how these clusters are embedded in the overall cortical architecture. For example, the ventral cluster of visual cortex maintains structurally more segregated, less divergent connections than the dorsal cluster, which may point to functionally different roles of their constituent brain regions.Comment: 17 pages, 6 figure

What are the Best Hierarchical Descriptors for Complex Networks?

This work reviews several hierarchical measurements of the topology of complex networks and then applies feature selection concepts and methods in order to quantify the relative importance of each measurement with respect to the discrimination between four representative theoretical network models, namely Erd\"{o}s-R\'enyi, Barab\'asi-Albert, Watts-Strogatz as well as a geographical type of network. The obtained results confirmed that the four models can be well-separated by using a combination of measurements. In addition, the relative contribution of each considered feature for the overall discrimination of the models was quantified in terms of the respective weights in the canonical projection into two dimensions, with the traditional clustering coefficient, hierarchical clustering coefficient and neighborhood clustering coefficient resulting particularly effective. Interestingly, the average shortest path length and hierarchical node degrees contributed little for the separation of the four network models.Comment: 9 pages, 4 figure

A Method for Characterizing Communities in Dynamic Attributed Complex Networks

Many methods have been proposed to detect communities, not only in plain, but also in attributed, directed or even dynamic complex networks. In its simplest form, a community structure takes the form of a partition of the node set. From the modeling point of view, to be of some utility, this partition must then be characterized relatively to the properties of the studied system. However, if most of the existing works focus on defining methods for the detection of communities, only very few try to tackle this interpretation problem. Moreover, the existing approaches are limited either in the type of data they handle, or by the nature of the results they output. In this work, we propose a method to efficiently support such a characterization task. We first define a sequence-based representation of networks, combining temporal information, topological measures, and nodal attributes. We then describe how to identify the most emerging sequential patterns of this dataset, and use them to characterize the communities. We also show how to detect unusual behavior in a community, and highlight outliers. Finally, as an illustration, we apply our method to a network of scientific collaborations.Comment: IEEE/ACM International Conference on Advances in Social Network Analysis and Mining (ASONAM), P\'ekin : China (2014