Related papers: Analyzing and modelling the AS-level Internet topo…
Large scale hierarchies characterize complex networks in different domains. Elements at their top, usually the most central or influential, may show multipolarization or tend to club forming tightly interconnected communities. The rich-club…
Integrated Gradients (IG) is a common explainability technique to address the black-box problem of neural networks. Integrated gradients assumes continuous data. Graphs are discrete structures making IG ill-suited to graphs. In this work,…
We present here a study of the clustering and cycles in the graph of Internet at the Autonomous Systems level. We show that,even if the whole structure is changing with time, the statistical distributions of loops of order 3,4,5 remain…
Many scale-free networks exhibit a rich club structure, where high degree vertices form tightly interconnected subgraphs. In this paper, we explore the emergence of rich clubs in the context of shortest path based centrality metrics. We…
Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on…
Graph neural networks (GNNs) are increasingly used to model biological systems, yet the reliability of post-hoc explanation methods for recovering meaningful molecular mechanisms remains unclear. Here, we systematically evaluate four widely…
We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…
The Autonomous System (AS) topology of the Internet (up to 61k ASs) is growing at a rate of about 10% per year. The Border Gateway Protocol (BGP) starts to show its limits in terms of the number of routing table entries it can dynamically…
A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood…
On-line social networks, such as in Facebook and Twitter, are often studied from the perspective of friendship ties between agents in the network. Adversarial ties, however, also play an important role in the structure and function of…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
The degree distributions of many real world networks follow power-laws whose exponents tend to fall between two and three. Within the framework of the Barabasi-Albert model (BA model), we explain this empirical observation by a simple fact.…
The Artificial Benchmark for Community Detection (ABCD) graph is a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs similar to the well-known LFR model…
A widely studied model for influence diffusion in social networks are {\it target sets}. For a graph $G$ and an integer-valued threshold function $\tau$ on its vertex set, a {\it target set} or {\it dynamic monopoly} is a set of vertices of…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
Various graph neural networks (GNNs) have been proposed to solve node classification tasks in machine learning for graph data. GNNs use the structural information of graph data by aggregating the features of neighboring nodes. However, they…
Based on solid theoretical foundations, we present strong evidences that a number of real-life networks, taken from different domains like Internet measurements, biological data, web graphs, social and collaboration networks, exhibit…
In complex networks, the rich-get-richer effect (nodes with high degree at one point in time gain more degree in their future) is commonly observed. In practice this is often studied on a static network snapshot, for example, a preferential…
Quantitative structure-activity relationship assumes a smooth relationship between molecular structure and biological activity. However, activity cliffs defined as pairs of structurally similar compounds with large potency differences break…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…