Related papers: Community Structure in Graphs
A network provides powerful means of representing complex relationships between entities by abstracting entities as vertices, and relationships as edges connecting vertices in a graph. Beyond the presence or absence of relationships, a…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Social relationships can be divided into different classes based on the regularity with which they occur and the similarity among them. Thus, rare and somewhat similar relationships are random and cause noise in a social network, thus…
Understanding community structures is crucial for analyzing networks, as nodes join communities that collectively shape large-scale networks. In real-world settings, the formation of communities is often impacted by several social factors,…
High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in…
A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that…
Networks and data supported on graphs have become ubiquitous in the sciences and engineering. This paper studies the 'blind' community detection problem, where we seek to infer the community structure of a graph model given the observation…
Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard…
Many times the nodes of a complex network, whether deliberately or not, are aggregated for technical, ethical, legal limitations or privacy reasons. A common example is the geographic position: one may uncover communities in a network of…
The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network…
A set of vertices in a graph is agile if, however we partition the set into two parts, we can always find two vertex-disjoint connected subgraphs where one covers the first and the other the second part. We present a characterization for…
We study how to detect groups in a complex network each of which consists of component nodes sharing a similar connection pattern. Based on the mixture models and the exploratory analysis set up by Newman and Leicht (Newman and Leicht 2007…
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…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
Social network analysis is pivotal for organizations aiming to leverage the vast amounts of data generated from user interactions on social media and other digital platforms. These interactions often reveal complex social structures, such…
Many social and biological networks consist of communities - groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting…
Complex real-world networks commonly reveal characteristic groups of nodes like communities and modules. These are of value in various applications, especially in the case of large social and information networks. However, while numerous…
Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…