Related papers: Termination of Multipartite Graph Series Arising f…
Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…
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 investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are…
Bipartite correlations in multi-qubit systems cannot be shared freely. The presence of entanglement or classical correlation on certain pairs of qubits may imply correlations on other pairs. We present a method of characterization of…
In the final project paper we consider a graph parameter called readability. Motivation for readability comes from bioinformatics applications. Graphs arising in problems related to genome sequencing are of small readability, which…
Extending the work of Godsil and others, we investigate the notion of the inverse of a graph (specifically, of bipartite graphs with a unique perfect matching). We provide a concise necessary and sufficient condition for the invertibility…
Quantum entanglement in multipartite systems cannot be shared freely. In order to illuminate basic rules of entanglement sharing between qubits we introduce a concept of an entangled structure (graph) such that each qubit of a multipartite…
We consider the problem of determining the maximal $\alpha \in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $\alpha |M|$. This measure was recently…
We consider the maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition or deletion of edges. When the set of edges in a graph changes, we are interested in knowing the change in the set of…
The bipartite graph structure has shown its promising ability in facilitating the subspace clustering and spectral clustering algorithms for large-scale datasets. To avoid the post-processing via k-means during the bipartite graph…
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…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…
The problem of identifying the maximum edge biclique in bipartite graphs has attracted considerable attention in bipartite graph analysis, with numerous real-world applications such as fraud detection, community detection, and online…
We consider dataflow architecture for two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We improve the earlier technique of almost continuous program…
Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet. In this paper, we propose a…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
The class of quasi-chain graphs is an extension of the well-studied class of chain graphs. This latter class enjoys many nice and important properties, such as bounded clique-width, implicit representation, well-quasi-ordering by induced…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…