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The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem (i) we propose a metric…
The notion of tree network has sparked renewed interest in recent years, particularly in computer science and biology (neural network). However, this notion is usually interpreted in an extremely restrictive way: essentially linked to data…
A network can be analyzed by means of many graph theoretical parameters. In the context of networks analysis, closeness is a structural metric that evaluates a node's significance inside a network. A cactus is a connected graph in which any…
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…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…
Composite systems are large complex systems con- sisting of interconnected agents (subsystems). Agents in a com- posite system interact with each other towards performing an in- tended goal. Controllability is essential to achieve desired…
Phylogenetic networks are used to study evolutionary relationships between species in biology. Such networks are often categorized into classes by their topological features, which stem from both biological and computational motivations. We…
Graph-structured data is ubiquitous in the world which models complex relationships between objects, enabling various Web applications. Daily influxes of unlabeled graph data on the Web offer immense potential for these applications. Graph…
For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two…
In this paper, several necessary and sufficient graphical conditions are derived for the controllability of multi-agent systems by taking advantage of the proposed concept of controllability destructive nodes. A key step of arriving at this…
Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee…
The human brain displays rich communication dynamics that are thought to be particularly well-reflected in its marked community structure. Yet, the precise relationship between community structure in structural brain networks and the…
In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected…
We present a new approach to edit distance attacks on certain clock-controlled generators, which applies basic concepts of Graph Theory to simplify the search trees of the original attacks in such a way that only the most promising branches…
We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even if we allow epsilon-contractions and reachability predicates (with regular constraints) for pairs of configurations, the structures remain…
We present a constraint model for the problem of producing a tree decomposition of a graph. The inputs to the model are a simple graph G, the number of nodes in the desired tree decomposition and the maximum cardinality of each node in that…
Attack trees (ATs) are popular graphical models for reasoning about the security of complex systems, allowing for the quantification of risk through so-called AT metrics. A large variety of different such AT metrics have been proposed, and…
Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool…
We study a graph-theoretic approach to the $\mathcal{H}_{\infty}$ performance of leader following consensus dynamics on directed and undirected graphs. We first provide graph-theoretic bounds on the system $\mathcal{H}_{\infty}$ norm of the…