相关论文: Giant components in directed multiplex networks
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
Order the vertices of a directed random graph \math{v_1,...,v_n}; edge \math{(v_i,v_j)} for \math{i<j} exists independently with probability \math{p}. This random graph model is related to certain spreading processes on networks. We…
We consider the strongly connected components (SCCs) of a uniform directed graph on $n$ vertices with i.i.d. in- and out-degree pairs distributed as $(D^-,D^+)$, with $\mathbb E[D^+]=\mathbb E[D^-]=\mu$. We condition on equal total in- and…
We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is…
The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder:…
Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
Deep directed generative models have attracted much attention recently due to their generative modeling nature and powerful data representation ability. In this paper, we review different structures of deep directed generative models and…
This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…
Finding strongly connected components (SCCs) and the diameter of a directed network play a key role in a variety of discrete optimization problems, and subsequently, machine learning and control theory problems. On the one hand, SCCs are…
Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous…
In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from practical points of view. In this contribution we present a module-based method to…
We consider networks with two types of nodes. The v-nodes, called centers, are hyper- connected and interact one to another via many u-nodes, called satellites. This central- ized architecture, widespread in gene networks, possesses two…
A network's assortativity is the tendency of vertices to bond with others based on similarities, usually excess vertex degree. In this paper we consider assortativity in weighted networks, both directed and undirected. To this end, we…
We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate…
Hidden geometry enables the investigation of complex networks at different scales. Extending this framework to multiplex networks, we uncover a novel kind of mesoscopic organization in real multiplex systems, named $\textit{clan}$, a group…
For decades, complex networks, such as social networks, biological networks, chemical networks, technological networks, have been used to study the evolution and dynamics of different kinds of complex systems. These complex systems can be…
The giant mutually connected component (GMCC) of an interdependent or multiplex network collapses with a discontinuous hybrid transition under random damage to the network. If the nodes to be damaged are selected in a targeted way, the…
Consider a random directed graph on $n$ vertices with independent identically distributed outdegrees with distribution $F$ having mean $\mu$, and destinations of arcs selected uniformly at random. We show that if $\mu >1$ then for large $n$…
The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In…