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We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-R\'enyi networks, based on recursion equations for the shells around a reference node and for the paths originating from…
The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the network is fully known, the shortest path problem can be…
In this paper, we investigate synchronization in a small-world network of coupled nonlinear oscillators. This network is constructed by introducing random shortcuts in a nearest-neighbors ring. The local stability of the synchronous state…
In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with…
In this report we show that in a planar exponentially growing network consisting of $N$ nodes, congestion scales as $O(N^2/\log(N))$ independently of how flows may be routed. This is in contrast to the $O(N^{3/2})$ scaling of congestion in…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
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…
Link prediction is a significant and challenging task in network science. The majority of known methods are similarity-based, which assign similarity indices for node pairs and assume that two nodes of larger similarity have higher…
We study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances. A particular case is where always the shortest distances are selected (``make friends with the friends of your…
Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…
When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
We introduce and explore a new method for inferring hidden geometric coordinates of nodes in complex networks based on the number of common neighbors between the nodes. We compare this approach to the HyperMap method, which is based only on…
In this paper we study the impact of degree correlations in the subgraphs statistics of scale-free networks. In particular we consider loops: a simple case of network subgraphs which encode the redundancy of the paths passing through every…
Recently, In [Phys. Rev. Lett. 104, 018701 (2010)] the authors studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is…
Symmetries found through automorphisms or graph fibrations provide important insights in network analysis. Symmetries identify clusters of robust synchronization in the network which improves the understanding of the functionality of…
Predicting links in complex networks has been one of the essential topics within the realm of data mining and science discovery over the past few years. This problem remains an attempt to identify future, deleted, and redundant links using…
Link prediction has become a critical problem in network science and has thus attracted increasing research interest. Popularity and similarity are two primary mechanisms in the formation of real networks. However, the roles of popularity…
Link prediction is one of the fundamental problems in network analysis. In many applications, notably in genetics, a partially observed network may not contain any negative examples of absent edges, which creates a difficulty for many…