Related papers: Series Parallel Linkages
In this work we present a dynamic analysis tool for analyzing regions of code and how those regions depend between each other via data dependencies encountered during the execution of the program. We also present an abstract method to…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…
A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
In this note we prove that every closed graph $G$ is up to isomorphism a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graph recognition.
An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…
We give a construction for a self-test for any connected graph state. In other words, for each connected graph state we give a set of non-local correlations that can only be achieved (quantumly) by that particular graph state and certain…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
In this article, we revisit and expand our prior work on graph similarity. As with our earlier work, we focus on a view of similarity which does not require node correspondence between graphs under comparison. Our work is suited to the…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
Graph (or network) is a mathematical structure that has been widely used to model relational data. As real-world systems get more complex, multilayer (or multiple) networks are employed to represent diverse patterns of relationships among…
We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that…
Recently, so-called treebased phylogenetic networks have gained considerable interest in the literature, where a treebased network is a network that can be constructed from a phylogenetic tree, called the base tree, by adding additional…
We examine spaces of connected tri-/univalent graphs subject to local relations which are motivated by the theory of Vassiliev invariants. It is shown that the behaviour of ladder-like subgraphs is strongly related to the parity of the…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…
We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all…