Related papers: Tree decompositions and social graphs
Retrieving cohesive subgraphs in networks is a fundamental problem in social network analysis and graph data management. These subgraphs can be used for marketing strategies or recommendation systems. Despite the introduction of numerous…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
Finding the dense regions in a graph is an important problem in network analysis. Core decomposition and truss decomposition address this problem from two different perspectives. The former is a vertex-driven approach that assigns density…
This paper deals with the construction of a correlation decay tree (hypertree) for interacting systems modeled using graphs (hypergraphs) that can be used to compute the marginal probability of any vertex of interest. Local message passing…
The structural cohesion model is a powerful theoretical conception of cohesion in social groups, but its diffusion in empirical literature has been hampered by operationalization and computational problems. In this paper we start from the…
As data are increasingly modeled as graphs for expressing complex relationships, the tree pattern query on graph-structured data becomes an important type of queries in real-world applications. Most practical query languages, such as XQuery…
Network design problems aim to compute low-cost structures such as routes, trees and subgraphs. Often, it is natural and desirable to require that these structures have small hop length or hop diameter. Unfortunately, optimization problems…
Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…
For a graph $G$, let $\Pi(G)$ denote the set of all potential maximal cliques of $G$. For each subset $\Pi$ of $\Pi(G)$, let $\tw(G, \Pi)$ denote the smallest $k$ such that there is a tree-decomposition of $G$ of width $k$ whose bags all…
Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from tree-like structures and the detection of hierarchical ordering remains a challenge, hindered by…
Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique,…
The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of leaves in T which correspond to edges…
With the recent explosion of publicly available biological data, the analysis of networks has gained significant interest. In particular, recent promising results in Neuroscience show that the way neurons and areas of the brain are…
Many data sets, crucial for today's applications, consist essentially of enormous networks, containing millions or even billions of elements. Having the possibility of visualizing such networks is of paramount importance. We propose an…
In the brain, the structure of a network of neurons defines how these neurons implement the computations that underlie the mind and the behavior of animals and humans. Provided that we can describe the network of neurons as a graph, we can…
We prove a general width duality theorem for combinatorial structures with well-defined notions of cohesion and separation. These might be graphs and matroids, but can be much more general or quite different. The theorem asserts a duality…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
This paper introduces a method to extract a hierarchical tree representation from 3D unorganized polygonal data. The proposed approach first extracts a graph representation of the surface, which serves as the foundation for structural…