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We explore the possibility to interpret as a 'gas' the dynamical self-organized scale-free network recently introduced by Kim et al (2005). The role of 'momentum' of individual nodes is played by the degree of the node, the 'configuration…

We consider hereditary classes of graphs equipped with a total order. We provide multiple equivalent characterisations of those classes which have bounded twin-width. In particular, we prove a grid theorem for classes of ordered graphs…

Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…

Random intersection graphs have received much attention for nearly two decades, and currently have a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. In this paper, we…

In this paper, we study commutative zero-divisor semigroups determined by graphs. We prove a uniqueness theorem for a class of graphs. We show two classes of graphs that have no corresponding semigroups. In particular, any complete graph…

Graph-based Anomaly Detection models have gained widespread adoption in recent years, identifying suspicious nodes by aggregating neighborhood information. However, most existing studies overlook the pervasive issues of missing and…

Graph anomaly detection aims to identify irregular patterns in graph-structured data. Most unsupervised GNN-based methods rely on the homophily assumption that connected nodes share similar attributes. However, real-world graphs often…

Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…

We address the problem of disentangled representation learning with independent latent factors in graph convolutional networks (GCNs). The current methods usually learn node representation by describing its neighborhood as a perceptual…

Real-world complex networks describe connections between objects; in reality, those objects are often endowed with some kind of features. How does the presence or absence of such features interplay with the network link structure? Although…

In this paper, we show that for any positive integer $m$ and $k\in [2]$, let $G$ be a $(2m+2k+2)$-connected graph and let $a_1,\ldots , a_m, s, t$ be any distinct vertices of $G$, there are $k$ internally disjoint $s$-$t$ paths $P_1,…

We describe a construction that maps any connected graph G on three or more vertices into a larger graph, H(G), whose independence number is strictly smaller than its Lov\'asz number which is equal to its fractional packing number. The…

In~\cite{bgs2013}, exclusion sensitivity and exclusion stability for symmetric exclusion processes on graphs were defined as a natural analogue of noise sensitivity and noise stability in this setting. As these concepts were defined for any…

Deterministic complex networks that use iterative generation algorithms have been found to more closely mirror properties found in real world networks than the traditional uniform random graph models. In this paper we introduce a new,…

We define a statistical ensemble of non-degenerate graphs, i.e. graphs without multiple- and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier…

Let $\mathcal G$ be an addable, minor-closed class of graphs. We prove that the zero-one law holds in monadic second-order logic (MSO) for the random graph drawn uniformly at random from all {\em connected} graphs in $\mathcal G$ on $n$…

Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Chickering (1995) provided a transformational characterization of…

Consider two data holders, ABC and XYZ, with graph data (e.g., social networks, e-commerce, telecommunication, and bio-informatics). ABC can see that node A is linked to node B, and XYZ can see node B is linked to node C. Node B is the…

In 2010, M. Studen\'y, R. Hemmecke, and S. Linder explored a new algebraic description of graphical models, called characteristic imsets. Compare with standard imsets, characteristic imsets have several advantages: they are still unique…

The problem of combinatorially determining the rank of the 3-dimensional bar-joint {\em rigidity matroid} of a graph is an important open problem in combinatorial rigidity theory. Maxwell's condition states that the edges of a graph $G=(V,…