Related papers: Self-similarity of Communities of the ABCD Model

In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…

The study of networks has received increased attention recently not only from the social sciences and statistics but also from physicists, computer scientists and mathematicians. One of the principal problem in networks is community…

Community detection is a very active field in complex networks analysis, consisting in identifying groups of nodes more densely interconnected relatively to the rest of the network. The existing algorithms are usually tested and compared on…

In complex networks, especially social networks, networks could be divided into disjoint partitions that the ratio between the number of internal edges (the edges between the vertices within same partition) to the number of outer edges…

Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e. the question of how good an algorithm…

Community detection in social networks is a problem with considerable interest, since, discovering communities reveals hidden information about networks. There exist many algorithms to detect inherent community structures and recently few…

Using methods from random matrix theory researchers have recently calculated the full spectra of random networks with arbitrary degrees and with community structure. Both reveal interesting spectral features, including deviations from the…

Graph models help understand network dynamics and evolution. Creating graphs with controlled topology and embedded partitions is a common strategy for evaluating community detection algorithms. However, existing benchmarks often overlook…

Laplacian eigenvectors capture natural community structures on graphs and are widely used in spectral clustering and manifold learning. The use of Laplacian eigenvectors as embeddings for the purpose of multiscale graph comparison has…

A degree-corrected distribution-free model is proposed for weighted social networks with latent structural information. The model extends the previous distribution-free models by considering variation in node degree to fit real-world…

No community detection algorithm can be optimal for all possible networks, thus it is important to identify whether the algorithm is suitable for a given network. We propose a multi-step algorithmic solution scheme for overlapping community…

We propose a novel method to test the existence of community structure of undirected real-valued edge-weighted graph. The method is based on Wigner semicircular law on the asymptotic behavior of the random distribution for eigenvalues of a…

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…

One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…

Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years,…

Community structure is of paramount importance for the understanding of complex networks. Consequently, there is a tremendous effort in order to develop efficient community detection algorithms. Unfortunately, the issue of a fair assessment…

Community structure is common in many real networks, with nodes clustered in groups sharing the same connections patterns. While many community detection methods have been developed for networks with binary edges, few of them are applicable…

Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes…

Communities in social networks or graphs are sets of well-connected, overlapping vertices. The effectiveness of a community detection algorithm is determined by accuracy in finding the ground-truth communities and ability to scale with the…

We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…