Related papers: Simpler and Unified Recognition Algorithm for Path…
Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…
This paper presents several algorithms for hashing directed graphs. The algorithms given are capable of hashing entire graphs as well as assigning hash values to specific nodes in a given graph. The notion of node symmetry is made precise…
We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…
The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
Let $P$ be a set of $n \geq 5$ points in convex position in the plane. The path graph $G(P)$ of $P$ is an abstract graph whose vertices are non-crossing spanning paths of $P$, such that two paths are adjacent if one can be obtained from the…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
In this paper, we define a class of auxiliary graphs associated with simple undirected graphs. This class of auxiliary graphs is based on the set of spanning trees of the original graph and the edges constituting those spanning trees. A…
We present a new fast all-pairs shortest path algorithm for unweighted graphs. In breadth-first search which is said to representative and fast in unweighted graphs, the average number of accesses to adjacent vertices (expressed by…
In this paper we consider the directed path-width and directed tree-width of recursively defined digraphs. As an important combinatorial tool, we show how the directed path-width and the directed tree-width can be computed for the disjoint…
A graph $G=(V,E)$ is a geometric intersection graph if every node $v \in V$ is identified with a geometric object of some particular type, and two nodes are adjacent if the corresponding objects intersect. Geometric intersection graph…
We propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. We argue that the previous…
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of…
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…
Protein subcellular localization is an important factor in normal cellular processes and disease. While many protein localization resources treat it as static, protein localization is dynamic and heavily influenced by biological context.…
We study graph classes modeled by families of non-crossing (NC) connected sets. Two classic graph classes in this context are disk graphs and proper interval graphs. We focus on the cases when the sets are paths and the host is a tree…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are just the opposite of taking minors. We show that some classes…
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…