Related papers: First-Order Model-Checking in Random Graphs and Co…

In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $\alpha_1$, a new vertex $x_t$ and $m$ edges…

We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail behaviour with exponent $\alpha+1$, where $\alpha \in (1,2)$. The limiting components are…

Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…

It is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-$r$ minors have constant density. More precisely, the formulas are $\exists x_1 ... x_k \#y…

Logical Neural Networks (LNNs) are a type of architecture which combine a neural network's abilities to learn and systems of formal logic's abilities to perform symbolic reasoning. LLNs provide programmers the ability to implicitly modify…

Random graph models are a recurring tool-of-the-trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test-bed generators for studying diffusion and…

Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…

Most random graph models are locally tree-like - do not contain short cycles - rendering them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the…

In recent years, researchers proposed several algorithms that compute metric quantities of real-world complex networks, and that are very efficient in practice, although there is no worst-case guarantee. In this work, we propose an…

First-order logic (FO) can express many algorithmic problems on graphs, such as the independent set and dominating set problem, parameterized by solution size. On the other hand, FO cannot express the very simple algorithmic question of…

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…

We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…

Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…

A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…

Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…

A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off…

Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these…

For a sequence of random structures with $n$-element domains over a relational signature, we define its first order (FO) complexity as a certain subset in the Banach space $\ell^{\infty}/c_0$. The well-known FO zero-one law and FO…

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…

Over the past two decades the main focus of research into first-order (FO) model checking algorithms has been on sparse relational structures - culminating in the FPT algorithm by Grohe, Kreutzer and Siebertz for FO model checking of…