Related papers: Clustering and the hyperbolic geometry of complex …

The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity…

A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…

Traditionally, graph quality metrics focus on readability, but recent studies show the need for metrics which are more specific to the discovery of patterns in graphs. Cluster analysis is a popular task within graph analysis, yet there is…

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. Clustering, community structure and assortative mixing by degree are perhaps among most prominent…

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between…

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…

We study here the clustering of directed social graphs. The clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…

The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…

Finding clusters of well-connected nodes in a graph is an extensively studied problem in graph-based data analysis. Because of its many applications, a large number of distinct graph clustering objective functions and algorithms have…

Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on…

Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical…

Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…

Many real-world networks display a natural bipartite structure. It is necessary and important to study the bipartite networks by using the bipartite structure of the data. Here we propose a modification of the clustering coefficient given…

Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these attributes and find that ensembles with strong clustering display both high assortativity by degree and prominent community…

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…

One way of getting a better view of data is using frequent patterns. In this paper frequent patterns are subsets that occur a minimal number of times in a stream of itemsets. However, the discovery of frequent patterns in streams has always…

The clustering property of complex networks indicates the abundance of small dense subgraphs in otherwise sparse networks. For a community-affiliation network defined by a superposition of Bernoulli random graphs, which has a nonvanishing…

Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic…