Notes for lecture given by the author on November 7, 2014 as part of the special course: “Randomness, Matrices and High Dimensional Problems”, at IMPA, Rio de Janeiro, Brazil. The results presented in these notes are from [1]. 1. The problem we will focus on Let n be an even positive integer. Given two sets of n2 nodes consider the following random graph G: For each pair (i, j) of nodes, (i, j)...

The problem and implications of community detection in networks have raised a huge attention, for its important applications in both natural and social sciences. A number of algorithms has been developed to solve this problem, addressing either speed optimization or the quality of the partitions calculated. In this paper we propose a multi-step procedure bridging the fastest, but less accurate ...

Community detection is a growing field of interest in the area of Social Network applications. Many community detection methods and surveys have been introduced in recent years, with each such method being classified according to its algorithm type. This chapter presents an original survey on this topic, featuring a new approach based on both semantics and type of output. Semantics opens up new...

Recent research has shown that virtually all algorithms aimed at the identification of communities in networks are affected by the same main limitation: the impossibility to detect communities, even when these are well-defined, if the average value of the difference between internal and external node degrees does not exceed a strictly positive value, in literature known as detectability thresho...

Traditional approaches to community detection, as studied by physicists, sociologists, and more recently computer scientists, aim at simply partitioning the social network graph. However, with the advent of online social networking sites, richer data has become available: beyond the link information, each user in the network is annotated with additional information, e.g., demographics, shopping...

The problem of community detection is a challenging one because of the presence of hubs and noisy links, which tend to create highly imbalanced graph clusters. Often, these resulting clusters are not very intuitive and difficult to interpret. With the growing availability of network information, there is a significant amount of prior knowledge available about the communities in social, communic...

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 size of the data. In this work, we provide three contributions. First, we show that a popular measure of accuracy known as the F1 score, which is between 0 a...

Multimodal clustering is an unsupervised technique for mining interesting patterns in n-adic binary relations or n-mode networks. Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed nsets for n-mode case, etc. Object-attribute biclustering (OA-biclustering) for min...

Community structure in networks indicates groups of vertices within which are dense connections and between which are sparse connections. Community detection, an important topic in data mining and social network analysis, has attracted considerable research interests in recent years. Motivated by the idea that community detection is in fact a clustering problem on graphs, we propose several sim...

Consider a network where the nodes split into K different communities. The community labels for the nodes are unknown and it is of major interest to estimate them (i.e., community detection). Degree Corrected Block Model (DCBM) is a popular network model. How to detect communities with the DCBM is an interesting problem, where the main challenge lies in the degree heterogeneity. We propose a ne...