Related papers: Absorbing random-walk centrality: Theory and algor…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Spanning Centrality is a measure used in network analysis to determine the importance of an edge in a graph based on its contribution to the connectivity of the entire network. Specifically, it quantifies how critical an edge is in terms of…
We consider a decentralized learning setting in which data is distributed over nodes in a graph. The goal is to learn a global model on the distributed data without involving any central entity that needs to be trusted. While gossip-based…
Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random…
Given a graph $G$, a query node $q$, and an integer $k$, community search (CS) seeks a cohesive subgraph (measured by community models such as $k$-core or $k$-truss) from $G$ that contains $q$. It is difficult for ordinary users with less…
Many real-world datasets have an underlying dynamic graph structure, where entities and their interactions evolve over time. Machine learning models should consider these dynamics in order to harness their full potential in downstream…
In this paper analogies between different (dis)similarity matrices are derived. These matrices, which are connected to path enumeration and random walks, are used in community detection methods or in computation of centrality measures for…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…
Various quantum-walk based algorithms have been proposed to analyse and rank the centrality of graph vertices. However, issues arise when working with directed graphs --- the resulting non-Hermitian Hamiltonian leads to non-unitary…
There has been a recent explosion in the size of stored data, partially due to advances in storage technology, and partially due to the growing popularity of cloud-computing and the vast quantities of data generated. This motivates the need…
The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…
Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of…
We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective…
In a network consisting of n nodes, our goal is to identify the most central k nodes with respect to the proposed definitions of centrality. Depending on the specific application, there exist several metrics for quantifying k-centrality,…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
We study the discrete-time quantum walk-based search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between the successful search probability and…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…