Related papers: When Is Degree Enough? Bounds on Degree-Eigenvecto…
Network science have constantly been in the focus of research for the last decade, with considerable advances in the controllability of their structural. However, much less effort has been devoted to study that how to improve the…
Networks are a popular tool for representing elements in a system and their interconnectedness. Many observed networks can be viewed as only samples of some true underlying network. Such is frequently the case, for example, in the…
The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum of given functions evaluated at the subgraph degrees. Here we study this problem by replacing degree sequences, via suitable nonlinear…
Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same network. Yet the structural reasons behind this…
Network alignment consists of finding a structure-preserving correspondence between the nodes of two correlated, but not necessarily identical, networks. This problem finds applications in a wide variety of fields, from the alignment of…
Transformer models have emerged as fundamental tools across various scientific and engineering disciplines, owing to their outstanding performance in diverse applications. Despite this empirical success, the theoretical foundations of…
We find that traditional statistics for measuring degree mixing are strongly affected by superrich nodes. To counteract and measure the effect of superrich nodes, we propose a paradigm to quantify the mixing pattern of a real network in…
The history of deep learning has shown that human-designed problem-specific networks can greatly improve the classification performance of general neural models. In most practical cases, however, choosing the optimal architecture for a…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
Extensive researches have been dedicated to investigating the performance of real networks and synthetic networks against random failures or intentional attack guided by degree (degree attack). Degree is one of straightforward measures to…
Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased…
We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…
Many real world networks, such as social networks, are primarily formed through local interactions between agents. Additionally, in contrast with common network models, social and biological networks exhibit a high degree of clustering.…
Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks.…
We present new degree-sequence lower bounds on the expected size of an independent set from the hard-core model. For arbitrary graphs, we establish a multivariate lower bound inspired by a conjecture of the first author and Kang and a…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
The results of training a neural network are heavily dependent on the architecture chosen; and even a modification of only its size, however small, typically involves restarting the training process. In contrast to this, we begin training…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
Degree ssortativity is the tendency for nodes of high degree (resp.low degree) in a graph to be connected to high degree nodes (resp. to low degree ones). It is sually quantified by the Pearson correlation coefficient of the degree-degree…