Related papers: The Fiedler connection to the parametrized modular…
One of the most remarkable social phenomena is the formation of communities in social networks corresponding to families, friendship circles, work teams, etc. Since people usually belong to several different communities at the same time,…
The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this…
Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a…
Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its…
Unknown node attributes in complex networks may introduce community structures that are important to distinguish from those driven by known attributes. We propose a block-corrected modularity that discounts given block structures present in…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
Detecting communities in networks and graphs is an important task across many disciplines such as statistics, social science and engineering. There are generally three different kinds of mixing patterns for the case of two communities:…
The analysis of temporal networks has a wide area of applications in a world of technological advances. An important aspect of temporal network analysis is the discovery of community structures. Real data networks are often very large and…
We develop a theory of ultrametric graphons as limiting objects for random networks with nested hierarchical community structure. A graphon $W:[0,1]^2\to[0,1]$ is called ultrametric if $W(x,y)=w(d(x,y))$, where $d$ is an ultrametric on…
We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time,…
The characterization of network community structure has profound implications in several scientific areas. Therefore, testing the algorithms developed to establish the optimal division of a network into communities is a fundamental problem…
We show that modularity maximization with the resolution parameter offers a unifying framework of graph partitioning. In this framework, we demonstrate that the spectral method exhibits universal detectability, irrespective of the value of…
We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix $A$. The result exploits the Frobenius inner product between $A$ and a given rank-one landmark matrix $X$. Different choices for $X$ may…
Many algorithms have been proposed for detecting disjoint communities (relatively densely connected subgraphs) in networks. One popular technique is to optimize modularity, a measure of the quality of a partition in terms of the number of…
We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or…
Community detection is a fundamental task in data analysis, and block models provide an approach for identifying a wide variety of community structures while offering high interpretability. The degree-corrected block model (DCBM) is an…
Community identification is a long-standing challenge in the modern network science, especially for very large scale networks containing millions of nodes. In this paper, we propose a new metric to quantify the structural similarity between…
The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block…
Many bipartite networks exhibit hierarchical community structure, but existing community detection methods are not well-suited for detecting hierarchy. They also do not effectively handle weighted bipartite networks. In this work, we…
A fundamental problem in mathematics and network analysis is to find conditions under which a graph can be partitioned into smaller pieces. The most important tool for this partitioning is the Fiedler vector or discrete Cheeger inequality.…