Related papers: Graph partitioning and a componentwise PageRank al…
The $k$th power of a graph $G$, denoted $G^k$, has the same vertex set as $G$, and two vertices are adjacent in $G^k$ if and only if there exists a path between them in $G$ of length at most $k$. A $K_r$-factor in a graph is a spanning…
Several organizations, like social networks, store and routinely analyze large graphs as part of their daily operation. Such graphs are typically distributed across multiple servers, and graph partitioning is critical for efficient graph…
Although research on the control of networked systems has grown considerably, graph-theoretic and algorithmic studies on matrix-weighted graphs remain limited. To bridge this gap in the literature, this work introduces two algorithms-the…
In order to improve system performance efficiently, a number of systems choose to equip multi-core and many-core processors (such as GPUs). Due to their discrete memory these heterogeneous architectures comprise a distributed system within…
A connected undirected graph $G=(V,E)$ is given. This paper presents an algorithm that samples (non-uniformly) a $K$ partition $U_1,\ldots U_K$ of the graph nodes $V$, such that the subgraph induced by each $U_k$, with $k=1:K$, is…
The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect…
The graph partitioning problem is a well-known NP-hard problem. In this paper, we formulate a 0-1 quadratic integer programming model for the graph partitioning problem with vertex weight constraints and fixed vertex constraints, and…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
We present the first linear-time algorithm that computes the $4$-edge-connected components of an undirected graph. Hence, we also obtain the first linear-time algorithm for testing $4$-edge connectivity. Our results are based on a…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge…
Graph classification has recently received a lot of attention from various fields of machine learning e.g. kernel methods, sequential modeling or graph embedding. All these approaches offer promising results with different respective…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
A graph that is completely determined by its degree sequence is called a unigraph. In 2000, Regina Tyshkevich published one of the most important papers on unigraphs. There are two parts to the paper: a decomposition theorem that describes…
Balanced graph partitioning is a critical step for many large-scale distributed computations with relational data. As graph datasets have grown in size and density, a range of highly-scalable balanced partitioning algorithms have appeared…
1-planar graphs are graphs that can be drawn in the plane such that any edge intersects with at most one other edge. Ackerman showed that the edges of a 1-planar graph can be partitioned into a planar graph and a forest, and claims that the…