Related papers: Hierarchical Random Graphs Based on Motifs
The presence of hierarchy in many real-world networks is not yet fully explained. Complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for…
The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present…
Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
Network motif analysis is a useful tool for the investigation of complex networks. We study the profiles of tetradic motifs in horizontal visibility graphs (HVGs) converted from multifractal binomial measures, fractional Gaussian noises,…
In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…
A growing set of applications consider the process of network formation by using subgraphs as a tool for generating the network topology. One of the pressing research challenges is thus to be able to use these subgraphs to understand the…
Activities such as the movement of passengers and goods, the transfer of physical or digital assets, web navigation and even successive passes in football, result in timestamped paths through a physical or virtual network. The need to…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
To any inhibition-dominated threshold-linear network (TLN) we can associate a directed graph that captures the pattern of strong and weak inhibition between neurons. Robust motifs are graphs for which the structure of fixed points in the…
Trends change rapidly in today's world, prompting this key question: What is the mechanism behind the emergence of new trends? By representing real-world dynamic systems as complex networks, the emergence of new trends can be symbolized by…
The statistical significance of network properties is conditioned on null models which satisfy spec- ified properties but that are otherwise random. Exponential random graph models are a principled theoretical framework to generate such…
We introduce two new bootstraps for exchangeable random graphs. One, the "empirical graphon bootstrap", is based purely on resampling, while the other, the "histogram bootstrap", is a model-based "sieve" bootstrap. We show that both of them…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
Frequent and structurally related subgraphs, also known as network motifs, are valuable features of many graph datasets. However, the high computational complexity of identifying motif sets in arbitrary datasets (motif mining) has limited…
Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific…
We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social…