Related papers: Spectral Detection of Simplicial Communities via H…

Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic…

The research on complex networks has achieved significant progress in revealing the mesoscopic features of networks. Community detection is an important aspect of understanding real-world complex systems. We present in this paper a…

Social relationships can be divided into different classes based on the regularity with which they occur and the similarity among them. Thus, rare and somewhat similar relationships are random and cause noise in a social network, thus…

The dynamical behavior of networked complex systems is shaped not only by the direct links among the units, but also by the long-range interactions occurring through the many existing paths connecting the network nodes. In this work, we…

Heterogeneous graphs have multiple node and edge types and are semantically richer than homogeneous graphs. To learn such complex semantics, many graph neural network approaches for heterogeneous graphs use metapaths to capture multi-hop…

Community detection is one of the most important problems in network analysis. Among many algorithms proposed for this task, methods based on statistical inference are of particular interest: they are mathematically sound and were shown to…

An ecological network is a formal representation of a specific type of interaction in a corresponding ecosystem. Such networks have traditionally been modelled as encoding exclusively pairwise interactions among the fundamental units of…

We first develop a general framework for Laplace operators defined in terms of the combinatorial structure of a simplicial complex. This includes, among others, the graph Laplacian, the combinatorial Laplacian on simplicial complexes, the…

Many networked datasets with units interacting in groups of two or more, encoded with hypergraphs, are accompanied by extra information about nodes, such as the role of an individual in a workplace. Here we show how these node attributes…

Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the…

Complex networks can model a range of different systems, from the human brain to social connections. Some of those networks have a large number of nodes and links, making it impractical to analyze them directly. One strategy to simplify…

In this work we introduce a concept of complexity for undirected graphs in terms of the spectral analysis of the Laplacian operator defined by the incidence matrix of the graph. Precisely, we compute the norm of the vector of eigenvalues of…

Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…

Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…

The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the…

We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not…

Community and cluster detection is a popular field of social network analysis. Most algorithms focus on static graphs or series of snapshots. In this paper we present an algorithm, which detects communities in dynamic graphs. The method is…

Community detection in networks is commonly performed using information about interactions between nodes. Recent advances have been made to incorporate multiple types of interactions, thus generalizing standard methods to multilayer…

Community detection and hierarchy extraction are usually thought of as separate inference tasks on networks. Considering only one of the two when studying real-world data can be an oversimplification. In this work, we present a generative…

We introduce an unsupervised graph embedding that trades off local node similarity and connectivity, and global structure. The embedding is based on a generalized graph Laplacian, whose eigenvectors compactly capture both network structure…