Related papers: Fixed-Point Centrality for Networks
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
This paper considers synchronous discrete-time dynamical systems on graphs based on the threshold model. It is well known that after a finite number of rounds these systems either reach a fixed point or enter a 2-cycle. The problem of…
This paper is centered on covariant dynamics on unimodular random graphs and random networks, namely maps from the set of vertices to itself which are preserved by graph or network isomorphisms. Such dynamics are referred to as…
We present a new general theory of function-based hypergraph transformations on finite families of finite hypergraphs. A function-based hypergraph transformation formalises the action of structurally modifying hypergraphs from a family in a…
The vertices of a $k$-token graph of a graph $G$ correspond to $k$ indistinguishable tokens placed on $k$ different vertices of $G$. Changing some conditions on both the nature of the tokens and the number of tokens allowed in each vertex…
Complex networks can be used to represent complex systems which originate in the real world. Here we study a transformation of these complex networks into simplicial complexes, where cliques represent the simplices of the complex. We extend…
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality…
Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been…
We present new values and bounds on the (normalised) closeness centrality $\bar{\mathsf{C}}_C$ of connected graphs and on its product $\bar{l}\bar{\mathsf{C}}_C$ with the mean distance $\bar{l}$ of these graphs. Our main result presents the…
Many real-world problems can be represented as graph-based learning problems. In this paper, we propose a novel framework for learning spatial and attentional convolution neural networks on arbitrary graphs. Different from previous…
Identifying critical nodes and links in graphs is a crucial task. These nodes/links typically represent critical elements/communication links that play a key role in a system's performance. However, a majority of the methods available in…
Adaptive (or co-evolutionary) network dynamics, i.e., when changes of the network/graph topology are coupled with changes in the node/vertex dynamics, can give rise to rich and complex dynamical behavior. Even though adaptivity can improve…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
Extracting information from real-world large networks is a key challenge nowadays. For instance, computing a node centrality may become unfeasible depending on the intended centrality due to its computational cost. One solution is to…
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…
Traditional convolutional neural networks are limited to handling Euclidean space data, overlooking the vast realm of real-life scenarios represented as graph data, including transportation networks, social networks, and reference networks.…
Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to…
This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…
Graph neural networks (GNNs) have achieved remarkable success in processing graph-structured data across various applications. A critical aspect of real-world graphs is their dynamic nature, where new nodes are continually added and…
Betweenness centrality is a centrality measure based on the overall amount of shortest paths passing through a given vertex. A graph is betweenness-uniform if all its vertices have the same betweenness centrality. We study the properties of…