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Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
Confining an answer to the question whether and how the coherent operation of network elements is determined by the the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the…
We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally…
The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…
The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…
An $n$-tuple $D=(d(1),\dots,d(n))$ is a \emph{feasible degree sequence} if there is a graph on $\{1,\dots,n\}$ such that $i$ has degree $d(i)$. Any such graph will have $m=\sum_{i=1}^n d(i)/2$ edges. Letting $G(D)$ be a graph chosen…
Network data is prevalent in many contemporary big data applications in which a common interest is to unveil important latent links between different pairs of nodes. Yet a simple fundamental question of how to precisely quantify the…
In this study, we focus on the likelihood ratio tests in the $p_0$ model for testing degree heterogeneity in directed networks, which is an exponential family distribution on directed graphs with the bi-degree sequence as the naturally…
Maximum entropy null models of networks come in different flavors that depend on the type of constraints under which entropy is maximized. If the constraints are on degree sequences or distributions, we are dealing with configuration…
Missing link prediction in indirected and un-weighted network is an open and challenge problem which has been studied intensively in recent years. In this paper, we studied the relationships between community structure and link formation…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set…
Predicting missing links in real networks is an important problem in network science to which considerable efforts have been devoted, giving as a result a vast plethora of link prediction methods in the literature. In this work, we take a…
It has been observed that many complex real-world networks have certain properties, such as a high clustering coefficient, a low diameter, and a power-law degree distribution. A network with a power-law degree distribution is known as…
Graph neural network (GNN) link prediction is increasingly deployed in citation, collaboration, and online social networks to recommend academic literature, collaborators, and friends. While prior research has investigated the dyadic…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
A bredge (bridge-edge) is an edge whose deletion would split the network component on which it resides into two components. Bredges are vulnerable links that play an important role in network collapse processes, which may result from node…
Let $d,n\in \mathbb{N}$ be such that $d=\omega(1)$, and $d\le n^{1-a}$ for some constant $a>0$. Consider a $d$-regular graph $G=(V, E)$ and the random graph process that starts with the empty graph $G(0)$ and at each step $G(i)$ is obtained…