Related papers: Tree decompositions and social graphs
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
The twin-width of a graph measures its distance to co-graphs and generalizes classical width concepts such as tree-width or rank-width. Since its introduction in 2020 (Bonnet et. al. 2020), a mass of new results has appeared relating twin…
We propose TD-GEN, a graph generation framework based on tree decomposition, and introduce a reduced upper bound on the maximum number of decisions needed for graph generation. The framework includes a permutation invariant tree generation…
Detecting strong ties among users in social and information networks is a fundamental operation that can improve performance on a multitude of personalization and ranking tasks. Strong-tie edges are often readily obtained from the social…
During the past decades significant efforts have been made to propose data structures for answering connectivity queries on fully dynamic graphs, i.e., graphs with frequent insertions and deletions of edges. However, a comprehensive…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this…
The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree depth. In this paper we survey results related to this concept…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
The discovery and analysis of network patterns are central to the scientific enterprise. In the present work, we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate…
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Social decisions made by individuals are easily influenced by information from their social neighborhoods. A key predictor of social contagion is the multiplicity of social contexts inside the individual's contact neighborhood, which is…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…
We introduce a decomposition method for the distributed calculation of exact Euclidean Minimum Spanning Trees in high dimensions (where sub-quadratic algorithms are not effective), or more generalized geometric-minimum spanning trees of…
Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…
The investigation of social networks is often hindered by their size as such networks often consist of at least thousands of vertices and edges. Hence, it is of major interest to derive compact structures that represent important…