相关论文: Generalized Cores
Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…
A retract of a graph $\Gamma$ is an induced subgraph $\Psi$ of $\Gamma$ such that there exists a homomorphism from $\Gamma$ to $\Psi$ whose restriction to $\Psi$ is the identity map. A graph is a core if it has no nontrivial retracts. In…
Cameron and Kazanidis have recently shown that rank-3 graphs are either cores or have complete cores, and they asked whether this holds for all strongly regular graphs. We prove that this is true for the point graphs and line graphs of…
Massive networks have shown that the determination of dense subgraphs, where vertices interact a lot, is necessary in order to visualize groups of common interest, and therefore be able to decompose a big graph into smaller structures. Many…
By identifying a local property which structurally classifies any edge, we show that the family of generalized Petersen graphs can be recognized in linear time.
Core decomposition is a fundamental operator in network analysis. In this paper, we study the problem of computing distance-generalized core decomposition on a network. A distance-generalized core, also termed $(k, h)$-core, is a maximal…
The core of a graph is the smallest graph (in terms of number of vertices) to which it is homomorphically equivalent. The question of the possible order of the core of the tensor product (also known as categorical, Heidetnemi or direct…
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…
Coreset (or core-set) is a small weighted \emph{subset} $Q$ of an input set $P$ with respect to a given \emph{monotonic} function $f:\mathbb{R}\to\mathbb{R}$ that \emph{provably} approximates its fitting loss $\sum_{p\in P}f(p\cdot x)$ to…
Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distributed linear operations, whose output depends only on the local…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral…
We use the k-core decomposition to visualize large scale complex networks in two dimensions. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by…
It is known that the vertex connectivity of a planar graph can be computed in linear time. We extend this result to the class of locally maximal 1-plane graphs: graphs that have an embedding with at most one crossing per edge such that the…
Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…
The concept of k-core in complex networks plays a key role in many applications, e.g., understanding the global structure, or identifying central/critical nodes, of a network. A malicious attacker with jamming ability can exploit the…
In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In…
We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph, as…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
We study an analogue of the classical moment problem in the framework where moments are indexed by graphs instead of natural numbers. We study limit objects of graph sequences where edges are labeled by elements of a topological space.…