Related papers: Node-neighbor subnetworks and Hk-core decompositio…

$k$-truss model is a typical cohesive subgraph model and has been received considerable attention recently. However, the $k$-truss model only considers the direct common neighbors of an edge, which restricts its ability to reveal…

Hypergraphs, graph generalizations where edges are conglomerates of $r$ nodes called hyperedges of rank $r\geq 2$, are excellent models to study systems with interactions that are beyond the pairwise level. For hypergraphs, the node degree…

Decomposition is a proven way to shrink deep networks without changing input-output dimensionality or interface semantics. We bring this idea to hyperdimensional computing (HDC), where footprint cuts usually shrink the feature axis and…

Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We…

In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator…

The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from…

Cycles are ubiquitous in various networks such as social, biological, and technological systems, where they play a significant functional and dynamical role. This paper proposes a node similarity measure based on minimal simple cycles,…

Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…

3D human pose estimation errors would propagate along the human body topology and accumulate at the end joints of limbs. Inspired by the backtracking mechanism in automatic control systems, we design an Intra-Part Constraint module that…

We develop a topological lens on relational schema design by encoding functional dependencies (FDs) as simplices of an abstract simplicial complex. This dependency complex exposes multi-attribute interactions and enables homological…

Motivated by the increasing interest in applications of graph geodesic convexity in machine learning and data mining, we present a heuristic for computing the geodesic convex hull of node sets in networks. It generates a set of almost…

Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…

Network community detection is a hot research topic in network analysis. Although many methods have been proposed for community detection, most of them only take into consideration the lower-order structure of the network at the level of…

Knowledge graph completion (KGC) aims to discover missing relations of query entities. Current text-based models utilize the entity name and description to infer the tail entity given the head entity and a certain relation. Existing…

We present a distributed algorithm to compute the first homology of a simplicial complex. Such algorithms are very useful in topological analysis of sensor networks, such as its coverage properties. We employ spanning trees to compute a…

The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…

Network reconstruction lies at the heart of phylogenetic research. Two well studied classes of phylogenetic networks include tree-child networks and level-$k$ networks. In a tree-child network, every non-leaf node has a child that is a tree…

This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…

Graph edit distance / similarity is widely used in many tasks, such as graph similarity search, binary function analysis, and graph clustering. However, computing the exact graph edit distance (GED) or maximum common subgraph (MCS) between…

Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this…