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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…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
Knowing which parts of a complex system have identical roles simplifies computations and reveals patterns in its network structure. Group theory has been applied to study symmetries in unweighted networks. However, in real-world weighted…
High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed…
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…
An isolating set in a graph is a set $X$ of vertices such that every edge of the graph is incident with a vertex of $X$ or its neighborhood. The isolation number of a graph, or equivalently the vertex-edge domination number, is the minimum…
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…
Successive whole genome duplications have recently been firmly established in all major eukaryote kingdoms. It is not clear, however, how such dramatic evolutionary process has contributed to shape the large scale topology of…
The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…
High-throughput protein interaction detection methods are strongly affected by false positive and false negative results. Focused experiments are needed to complement the large-scale methods by validating previously detected interactions…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Proteins participating in a protein-protein interaction network can be grouped into homology classes following their common ancestry. Proteins added to the network correspond to genes added to the classes, so that the dynamics of the two…
We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability can be lost with high probability when matching the networks…
The study of epidemic spreading on populations of networked individuals has seen recently a great deal of significant progresses. A common point of all past studies is, however, that there is only one peak of infected density in each single…
We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…
The behavior of the leading singular values and vectors of noisy low-rank matrices is fundamental to many statistical and scientific problems. Theoretical understanding currently derives from asymptotic analysis under one of two regimes:…
Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…
We find large deviation principles for the degree distribution and the proportion of isolated vertices for the near intermediate random geometric graph models on n vertices placed uniformly in [0, 1]^d, for d in N. In the course of the…
A method that reconstructs protein residue networks using suitable node selection and edge recovery policies produced numerical observations that correlate strongly (Pearson's correlation coefficient < -0.83) with published folding rates…