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Models of growing networks are a central topic in network science. In these models, vertices are usually labeled by their arrival time, distinguishing even those node pairs whose structural roles are identical. In contrast, unlabeled…
Knowledge graphs play a central role for linking different data which leads to multiple layers. Thus, they are widely used in big data integration, especially for connecting data from different domains. Few studies have investigated the…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
Graph neural networks (GNNs) can process graphs of different sizes, but their ability to generalize across sizes, specifically from small to large graphs, is still not well understood. In this paper, we identify an important type of data…
We study the power of \textit{local information algorithms} for optimization problems on social networks. We focus on sequential algorithms for which the network topology is initially unknown and is revealed only within a local neighborhood…
A Locally Checkable Labeling (LCL) is a specification describing a set of labels that are valid with respect to a set of conditions that characterize a local part of a solution to a global problem. Conditions can only refer to nodes and…
In practice, since many communication networks are huge in scale, or complicated in structure, or even dynamic, the predesigned linear network codes based on the network topology is impossible even if the topological structure is known.…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…
In this paper we study the controllability of networked systems with static network topologies using tools from algebraic graph theory. Each agent in the network acts in a decentralized fashion by updating its state in accordance with a…
The local tree-width of a graph G=(V,E) is the function ltw^G: N -> N that associates with every natural number r the maximal tree-width of an r-neighborhood in G. Our main graph theoretic result is a decomposition theorem for graphs with…
Recently a distributed algorithm has been proposed for multi-agent networks to solve a system of linear algebraic equations, by assuming each agent only knows part of the system and is able to communicate with nearest neighbors to update…
We define notions of local topological convergence and local geometric convergence for embedded graphs in $\mathbb{R}^n,$ and study their properties. The former is related to Benjamini-Schramm convergence, and the latter to weak convergence…
In this paper, we derive nonasymptotic theoretical bounds for the influence in random graphs that depend on the spectral radius of a particular matrix, called the Hazard matrix. We also show that these results are generic and valid for a…
Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…
Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two…
Consider a computer network that consists of a path with $n$ nodes. The nodes are labeled with inputs from a constant-sized set, and the task is to find output labels from a constant-sized set subject to some local constraints---more…
The loss surface of deep neural networks has recently attracted interest in the optimization and machine learning communities as a prime example of high-dimensional non-convex problem. Some insights were recently gained using spin glass…
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…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…