Related papers: The missing links in the BGP-based AS connectivity…
Link prediction is a fundamental problem in graph data. In its most realistic setting, the problem consists of predicting missing or future links between random pairs of nodes from the set of disconnected pairs. Graph Neural Networks (GNNs)…
In this paper, we investigate the exact asymptotic behavior of the connectivity probability in the Erdos-Renyi graph G(n,p), under different asymptotic assumptions on the edge probability p=p(n). We propose a novel approach based on the…
This work presents conjectures about eigenvalues of matrices associated with $k$-path graphs, the algebraic connectivity, defined as the second smallest eigenvalue of the Laplacian matrix, and the $\alpha$-index, as the largest eigenvalue…
Predicting missing links in complex networks requires algorithms that are able to explore statistical regularities in the existing data. Here we investigate the interplay between algorithm efficiency and network structures through the…
Community structure exists in many real-world networks and has been reported being related to several functional properties of the networks. The conventional approach was partitioning nodes into communities, while some recent studies start…
We study the geometry and topology of real analytic maps $\mathbb{C}^n \to \mathbb{C}^k$, where $n > k$, regarded as mixed maps, defined below. Firstly, we give two natural families of mixed isolated complete intersection singularities,…
The r-th power of a graph modifies a graph by connecting every vertex pair within distance r. This paper gives a generalization of the Alon-Boppana Theorem for the r-th power of graphs, including irregular graphs. This leads to a…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
Network alignment is the problem of matching the nodes of two graphs, maximizing the similarity of the matched nodes and the edges between them. This problem is encountered in a wide array of applications-from biological networks to social…
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…
We study the size of the largest biconnected components in sparse Erd\H{o}s-R\'enyi graphs with finite connectivity and Barab\'asi-Albert graphs with non-integer mean degree. Using a statistical-mechanics inspired Monte Carlo approach we…
This paper studies the problem of increasing the connectivity of an ad-hoc peer-to-peer network subject to cyber-attacks targeting the agents in the network. The adopted strategy involves the design of local interaction rules for the agents…
Fiber graphs of Gr\"obner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The connectivity of the graphs has implications…
What is the impact of obstacles on the graphs of connections between stations in Mobile Ad hoc Networks? In order to answer, at least partially, this question, the first step is to define both an environment with obstacles and a mobility…
A labelled, undirected graph is a graph whose edges have assigned labels, from a specific set. Given a labelled, undirected graph, the well-known minimum labelling spanning tree problem is aimed at finding the spanning tree of the graph…
Rich-club ordering refers to the tendency of nodes with a high degree to be more interconnected than expected. In this paper we consider the concept of rich-club ordering when generalized to structural measures that differ from the node…
Traffic congestion in isolated complex networks has been investigated extensively over the last decade. Coupled network models have recently been developed to facilitate further understanding of real complex systems. Analysis of traffic…
The Price model, the directed version of the Barab\'{a}si-Albert model, produces a growing directed acyclic graph. We look at variants of the model in which directed edges are added to the new vertex in one of two ways: using cumulative…
The explosive growth of Web 2.0, which was characterized by the creation of online social networks, has reignited the study of factors that could help us understand the growth and dynamism of these networks. Various generative network…
In many applications, researchers seek to identify overlapping entities across multiple data files. Record linkage algorithms facilitate this task, in the absence of unique identifiers. As these algorithms rely on semi-identifying…