Related papers: Topology recognition with advice
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
We summarize the main results proved in recent work on the parameterized verification of safety properties for ad hoc network protocols. We consider a model in which the communication topology of a network is represented as a graph. Nodes…
Consider a network of agents that all want to guess the correct value of some ground truth state. In a sequential order, each agent makes its decision using a single private signal which has a constant probability of error, as well as…
Signal processing and machine learning algorithms for data supported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the…
Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…
Pooling operations have shown to be effective on computer vision and natural language processing tasks. One challenge of performing pooling operations on graph data is the lack of locality that is not well-defined on graphs. Previous…
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
In the voter model, each node of a graph has an opinion, and in every round each node chooses independently a random neighbour and adopts its opinion. We are interested in the consensus time, which is the first point in time where all nodes…
Measuring the topological overlap of two graphs becomes important when assessing the changes between temporally adjacent graphs in a time-evolving network. Current methods depend on the fraction of nodes that have persisting edges. This…
Passive network tomography uses end-to-end observations of network communication to characterize the network, for instance to estimate the network topology and to localize random or adversarial glitches. Under the setting of linear network…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
Limited presence of nodal and line meters in distribution grids hinders their optimal operation and participation in real-time markets. In particular lack of real-time information on the grid topology and infrequently calibrated line…
The key towards learning informative node representations in graphs lies in how to gain contextual information from the neighbourhood. In this work, we present a simple-yet-effective self-supervised node representation learning strategy via…
We propose an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected graphs with cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian.…
The sorting number of a graph with $n$ vertices is the minimum depth of a sorting network with $n$ inputs and outputs that uses only the edges of the graph to perform comparisons. Many known results on sorting networks can be stated in…
Recommendation plays a key role in e-commerce and in the entertainment industry. We propose to consider successive recommendations to users under the form of graphs of recommendations. We give models for this representation. Motivated by…
The number of nodes of a network, called its size, and the largest distance between nodes of a network, called its diameter, are among the most important network parameters. Knowing the size and/or diameter is a prerequisite of many…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
A wide range of networks, including small-world topology, can be modelled by the connectivity $\gamma$, and randomness $\omega$ of the links. Both learning and attractor abilities of a neural network can be measured by the mutual…
Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the…