Related papers: Exponential Generalised Network Descriptors
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…
Many biological, ecological and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most network models studied so far are binary, the link strength being either 0…
A network's assortativity is the tendency of vertices to bond with others based on similarities, usually excess vertex degree. In this paper we consider assortativity in weighted networks, both directed and undirected. To this end, we…
Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…
Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be…
This work reviews several hierarchical measurements of the topology of complex networks and then applies feature selection concepts and methods in order to quantify the relative importance of each measurement with respect to the…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
Interpreting natural language is an increasingly important task in computer algorithms due to the growing availability of unstructured textual data. Natural Language Processing (NLP) applications rely on semantic networks for structured…
We introduce the concept of communicability angle between a pair of nodes in a graph. We provide strong analytical and empirical evidence that the average communicability angle for a given network accounts for its spatial efficiency on the…
We address two fundamental questions about graph neural networks (GNNs). First, we prove that several important graph properties cannot be computed by GNNs that rely entirely on local information. Such GNNs include the standard message…
Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years a multitude of diverse, ad hoc solutions to this problem have been introduced. Here we propose that simple and…
Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…
With the advance of efficient analytical methods for sensitivity analysis ofprobabilistic networks, the interest in the sensitivities revealed by real-life networks is rekindled. As the amount of data resulting from a sensitivity analysis…
We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…
Research on the vulnerability of electric networks with a complex network approach has produced significant results in the last decade, especially for transmission networks. These studies have shown that there are causal relations between…
The links of a physical network cannot cross, which often forces the network layout into non-optimal entangled states. Here we define a network fabric as a two-dimensional projection of a network and propose the average crossing number as a…
Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…
Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…