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Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…

Downsampling produces coarsened, multi-resolution representations of data and it is used, for example, to produce lossy compression and visualization of large images, reduce computational costs, and boost deep neural representation…

Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are…

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…

The study of complex networks has been historically based on simple graph data models representing relationships between individuals. However, often reality cannot be accurately captured by a flat graph model. This has led to the…

To understand the structure of a network, it can be useful to break it down into its constituent pieces. This is the approach taken in a multitude of successful network analysis methods, such as motif analysis. These methods require one to…

It has been discovered that Graph Convolutional Networks (GCNs) encounter a remarkable drop in performance when multiple layers are piled up. The main factor that accounts for why deep GCNs fail lies in over-smoothing, which isolates the…

Regularization is an important component of predictive model building. The hybrid bootstrap is a regularization technique that functions similarly to dropout except that features are resampled from other training points rather than replaced…

It is known that the current graph neural networks (GNNs) are difficult to make themselves deep due to the problem known as over-smoothing. Multi-scale GNNs are a promising approach for mitigating the over-smoothing problem. However, there…

The design of robust supply and distribution systems is one of the fundamental challenges at the interface of network science and logistics. Given the multitude of performance criteria, real-world constraints, and external influences acting…

Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…

We introduce a novel view to understand how dropout works as an inexplicit ensemble learning method, which doesn't point out how many and which nodes to learn a certain feature. We propose a new training method named internal node bagging,…

Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…

We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neural networks (DNNs). DNNs show remarkable generalization…

Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…

Graph Neural Networks (GNNs) are powerful tools for handling graph-type data. Recently, GNNs have been widely applied in various domains, but they also face some issues, such as overfitting, over-smoothing and non-robustness. The existing…

Structure inference is an important task for network data processing and analysis in data science. In recent years, quite a few approaches have been developed to learn the graph structure underlying a set of observations captured in a data…

In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…

Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…

Due to lack of data, overfitting ubiquitously exists in real-world applications of deep neural networks (DNNs). We propose advanced dropout, a model-free methodology, to mitigate overfitting and improve the performance of DNNs. The advanced…