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In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the node's importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e.…
Node similarity scores are a foundation for machine learning in graphs for clustering, node classification, anomaly detection, and link prediction with applications in biological systems, information networks, and recommender systems.…
Immunizing a subset of nodes in a network - enabling them to identify and withstand the spread of harmful content - is one of the most effective ways to counter the spread of malicious content. It has applications in network security,…
This paper discusses the enumeration of two-terminal series-parallel networks, i.e. the number of electrical networks built with n identical elements connected in series or parallel with two-terminal nodes. They frequently occur in applied…
We consider the problem of maximizing the algebraic connectivity of the communication graph in a network of mobile robots by moving them into appropriate positions. We define the Laplacian of the graph as dependent on the pairwise distance…
The problem of link prediction, predicting if two nodes in a network have a connection between them, is a theoretical problem with numerous field-agnostic real-world applications. This paper investigates the efficacy of three classes of…
Cycles are ubiquitous in various networks such as social, biological, and technological systems, where they play a significant functional and dynamical role. This paper proposes a node similarity measure based on minimal simple cycles,…
The simplest null models for networks, used to distinguish significant features of a particular network from {\it a priori} expected features, are random ensembles with the degree sequence fixed by the specific network of interest. These…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
Missing link prediction of networks is of both theoretical interest and practical significance in modern science. In this paper, we empirically investigate a simple framework of link prediction on the basis of node similarity. We compare…
Undirected hyperbolic graph models have been extensively used as models of scale-free small-world networks with high clustering coefficient. Here we presented a simple directed hyperbolic model, where nodes randomly distributed on a…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
We consider network design problems in which we are given a graph and seek a min-size $2$-connected subgraph that satisfies a prescribed property. $\bullet$ In the 1-Connectivity Augmentation problem the goal is to augment a connected graph…
The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the…
We propose that negative degree correlation among nodes in a network of nonlinear oscillators, often detected in real world networks, is motivated by its positive effects on synchronizability. In so doing, we use a novel methodology to…
Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…
Evaluation of link prediction methods is a hard task in very large complex networks because of the inhibitive computational cost. By setting a lower bound of the number of common neighbors (CN), we propose a new framework to efficiently and…