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Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
Reciprocity in social networks helps understand information exchange between two individuals, and indicates interaction patterns between pairs of users. A recent study indicates the reciprocity coefficient of a classical directed…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
Networks are widely used to model the contact structure within a population and in the resulting models of disease spread. While networks provide a high degree of realism, the analysis of the exact model is out of reach and even numerical…
The lack of studying the complex organization of directed network usually limits to the understanding of underlying relationship between network structures and functions. Structural controllability and structural predictability, two…
We address the problem of link reciprocity, the non-random presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation…
This paper proposes a simple procedure to decide whether the empirically-observed adjacency or weights matrix, which characterizes the graph underlying a socio-economic network, is sufficiently symmetric (respectively, asymmetric) to…
Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our…
Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is commonly focalised on edge processes, and a dual edge-centric perspective can…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…
Structural balance theory predicts that triads in networks gravitate towards stable configurations. The theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for…