Related papers: Network Global Testing by Counting Graphlets

Although community detection has drawn tremendous amount of attention across the sciences in the past decades, no formal consensus has been reached on the very nature of what qualifies a community as such. In this article we take an…

Graph mining has become crucial in fields such as social science, finance, and cybersecurity. Many large-scale real-world networks exhibit both heterogeneity, where multiple node and edge types exist in the graph, and heterophily, where…

Classical results on the statistical complexity of linear models have commonly identified the norm of the weights $\|w\|$ as a fundamental capacity measure. Generalizations of this measure to the setting of deep networks have been varied,…

Social Network Analysis is the use of Network and Graph Theory to study social phenomena, which was found to be highly relevant in areas like Criminology. This chapter provides an overview of key methods and tools that may be used for the…

Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed-memberships, (c) have a…

The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its…

A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based…

Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…

With the rapid development of information technologies, various big graphs are prevalent in many real applications (e.g., social media and knowledge bases). An important component of these graphs is the network community. Essentially, a…

Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…

Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…

Conventional network data has largely focused on pairwise interactions between two entities, yet multi-way interactions among multiple entities have been frequently observed in real-life hypergraph networks. In this article, we propose a…

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…

Graph centrality measures use the structure of a network to quantify central or "important" nodes, with applications in web search, social media analysis, and graphical data mining generally. Traditional centrality measures such as the well…

We give a construction for a self-test for any connected graph state. In other words, for each connected graph state we give a set of non-local correlations that can only be achieved (quantumly) by that particular graph state and certain…

Exploring small connected and induced subgraph patterns (CIS patterns, or graphlets) has recently attracted considerable attention. Despite recent efforts on computing the number of instances a specific graphlet appears in a large graph…

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…

Machine learning models that learn from dynamic graphs face nontrivial challenges in learning and inference as both nodes and edges change over time. The existing large-scale graph benchmark datasets that are widely used by the community…