相关论文: Core-satellite Graphs. Clustering, Assortativity a…

Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…

We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and…

This paper is partly a report on current knowledge concerning the structure of (generic) quantized coordinate rings and their prime spectra, and partly propaganda in support of the conjecture that since these algebras share many common…

We develop a theory of average sizes of kernels of generic matrices with support constraints defined in terms of graphs and hypergraphs. We apply this theory to study unipotent groups associated with graphs. In particular, we establish…

Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…

In this note, we present a structural description of certain connected cographs having $k \geq 2$ main signless Laplacian eigenvalues. This result allows us to characterize the cographs which are quasi-threshold graphs with two main…

Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…

We investigate properties that intuitively ought to be satisfied by graph clustering quality functions, that is, functions that assign a score to a clustering of a graph. Graph clustering, also known as network community detection, is often…

We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…

A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…

We introduce new centrality measures, called ksi-centrality and normalized ksi-centrality measure the importance of a node up to the importance of its neighbors. First, we show that normalized ksi-centrality can be rewritten in terms of the…

We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…

We present a graph-theoretical approach to data clustering, which combines the creation of a graph from the data with Markov Stability, a multiscale community detection framework. We show how the multiscale capabilities of the method allow…

We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…

We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…

While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and…

Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi-Albert (BA) Scale-Free model with both analytical results and simulations, and find…

Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by…

The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…