Related papers: Structural Balance of Complex Weighted Graphs and …
Signed networks are such social networks having both positive and negative links. A lot of theories and algorithms have been developed to model such networks (e.g., balance theory). However, previous work mainly focuses on the unipartite…
The concept of graph powers has been extensively studied in graph theory. Analogous to graph powers, Chandran et al. [3] introduced the notion of bipartite powers for bipartite graphs. In this paper, we show that the class of interval…
We consider the problem of multi-agent consensus where some agents are subject to faults/attacks and might make updates arbitrarily. The network consists of agents taking integer-valued (i.e., quantized) states under directed communication…
This paper considers the resilient multi-dimensional consensus problem in networked systems, where some of the agents might be malicious (or faulty). We propose a multi-dimensional consensus algorithm, where at each time step each healthy…
This paper studies a consensus problem of multi-agent systems subjected to external disturbances over the clustered network. It considers that the agents are divided into several clusters. They are almost all the time isolated one from…
Property $(P)$, introduced in recent work and rooted in the classical theory of Parter vertices, concerns the existence of a nonsingular matrix $A\in S(G)$ for which every vertex of $G$ is a $P$-vertex. Previous investigations have fully…
Given a bipartite graph that has a perfect matching, a prefect proportional allocation is an assignment of positive weights to the nodes of the right partition so that every left node is fractionally assigned to its neighbors in proportion…
We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of bipartite graphs of given…
This work addresses the edge-based synchronization problem in first-order multi-agent systems containing both cooperative and antagonistic interactions with one or multiple leader groups. The presence of multiple leaders and antagonistic…
Multi agent consensus algorithms with update steps based on so-called balanced asymmetric chains, are analyzed. For such algorithms it is shown that (i) the set of accumulation points of states is finite, (ii) the asymptotic unconditional…
In this work we consider a collective decision-making process in a network of agents described by a nonlinear interconnected dynamical model with sigmoidal nonlinearities and signed interaction graph. The decisions are encoded in the…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
Multi-layer graphs can capture qualitatively different types of connection between entities, and networks of this kind are prevalent in biological and social systems: for example, a social contact network typically involves both virtual and…
Consensusability of multi-agent systems (MASs) certifies the existence of a distributed controller capable of driving the states of each subsystem to a consensus value. We study the consensusability of linear interconnected MASs (LIMASs)…
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…
Structural balance theory studies stability in networks. Given a $n$-vertex complete graph $G=(V,E)$ whose edges are labeled positive or negative, the graph is considered \emph{balanced} if every triangle either consists of three positive…
The topic of stable matchings (marriages) in a bipartite graph has become widely popular, starting with the appearance of the classical work by Gale and Shapley. We give a detailed survey on selected known results in this field that…
We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrix- and graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite…
Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This…