Related papers: Determining X-chains in graph states

Consider observations $y_1,\dots,y_n$ on nodes of a connected graph, where the $y_i$ independently come from $N(\theta_i, \sigma^2)$ distributions and an unknown partition divides the $n$ observations into blocks. One well-studied class of…

Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…

Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…

Several families of states such as Werner states, Bell-diagonal states and Dicke states are useful to understand multipartite entanglement. Here we present a [2^(N+1)-1]-parameter family of N-qubit "X states" that embrace all those…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

We give a sufficient and necessary condition for a Praeger-Xu graph to be a Cayley graph.

Let H = (V,E) be a k-uniform hypergraph with a vertex set V and an edge set E. Let V_p be constructed by taking every vertex in V independently with probability p. Let X be the number of edges in E that are contained in V_p. We give a…

A 2-edge-coloured graph $G$ is {\bf supereulerian} if $G$ contains a spanning closed trail in which the edges alternate in colours. An {\bf eulerian factor} of a 2-edge-coloured graph is a collection of vertex disjoint induced subgraphs…

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in…

Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…

With the increased complexity of power systems due to the integration of smart grid technologies and renewable energy resources, more frequent changes have been introduced to system status, and the traditional serial mode of state…

We develop a notion of containment for independent sets in hypergraphs. For every $r$-uniform hypergraph $G$, we find a relatively small collection $C$ of vertex subsets, such that every independent set of $G$ is contained within a member…

Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…

We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrix- and graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite…

Given a large social or computer network, how can we visualize it, find patterns, outliers, communities? Although several graph visualization tools exist, they cannot handle large graphs with hundred thousand nodes and possibly million…

Community detection is of great importance for understand-ing graph structure in social networks. The communities in real-world networks are often overlapped, i.e. some nodes may be a member of multiple clusters. How to uncover the…

The abundance of interconnected data has fueled the design and implementation of graph generators reproducing real-world linking properties, or gauging the effectiveness of graph algorithms, techniques and applications manipulating these…

We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-Z gates. We study the entanglement features of…

This extended abstract introduces a class of graph learning applicable to cases where the underlying graph has polytopic uncertainty, i.e., the graph is not exactly known, but its parameters or properties vary within a known range. By…

Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…