Maximum Estrada Index of Bicyclic Graphs

Let $G$ be a simple graph of order $n$, let $\lambda_1(G),\lambda_2(G),...,\lambda_n(G)$ be the eigenvalues of the adjacency matrix of $G$. The Esrada index of $G$ is defined as $EE(G)=\sum_{i=1}^{n}e^{\lambda_i(G)}$. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order

Metaplex networks: influence of the exo-endo structure of complex systems on diffusion

In a complex system the interplay between the internal structure of its entities and their interconnection may play a fundamental role in the global functioning of the system. Here, we define the concept of metaplex, which describes such trade-off between internal structure of entities and their interconnections. We then define a dynamical system on a metaplex and study diffusive processes on them. We provide analytical and computational evidences about the role played by the size of the nodes, the location of the internal coupling areas, and the strength and range of the coupling between the nodes on the global dynamics of metaplexes. Finally, we extend our analysis to two real-world metaplexes: a landscape and a brain metaplex. We corroborate that the internal structure of the nodes in a metaplex may dominate the global dynamics (brain metaplex) or play a regulatory role (landscape metaplex) to the influence of the interconnection between nodes.Comment: 28 pages, 19 figure

Communicability Angles Reveal Critical Edges for Network Consensus Dynamics

We consider the question of determining how the topological structure influences a consensus dynamical process taking place on a network. By considering a large dataset of real-world networks we first determine that the removal of edges according to their communicability angle -an angle between position vectors of the nodes in an Euclidean communicability space- increases the average time of consensus by a factor of 5.68 in real-world networks. The edge betweenness centrality also identifies -in a smaller proportion- those critical edges for the consensus dynamics, i.e., its removal increases the time of consensus by a factor of 3.70. We justify theoretically these findings on the basis of the role played by the algebraic connectivity and the isoperimetric number of networks on the dynamical process studied, and their connections with the properties mentioned before. Finally, we study the role played by global topological parameters of networks on the consensus dynamics. We determine that the network density and the average distance-sum -an analogous of the node degree for shortest-path distances, account for more than 80% of the variance of the average time of consensus in the real-world networks studied.Comment: 15 pages, 2 figure

Insider trading: regulation, securities markets, and welfare under risk neutrality

I evaluate in this paper the impact of insider trading regulation (ITR) on a securities market and on social welfare. I show that ITR has both beneficial and detrimental effects on a securities market. In terms of welfare, I show that ITR has a purely redistributive effect; that is, it generates trading gains and trading losses that cancel out at the aggregate level. However, the goods and services that could have been produced with the resources allocated to enforce such a wealth redistribution are a net social cost of restricting insider trading. Finally, although I establish two conditions under which ITR is beneficial, I argue that neither condition provides sufficient support to the imposition of such a regulation

Crime and punishment: An introductory analysis in a noncooperative framework

The purpose of this paper is twofold. First, it seeks to provide the unsophisticated reader with an introduction to modelling issues of crime and punishment; and, second, it seeks to introduce a noncooperative analytical framework as the basic modelling technique to analyze issues of crime and punishment. To those purposes, I introduce a simple model from which important policy recommendations follow from the noncooperative interaction between criminals and the rest of society

Insider trading: regulation, securities markets, and welfare under risk aversion

I analyze in this paper the impact of insider trading regulation (ITR) on a securities market and on social welfare. I argue below that the imposition of ITR forces a reallocation of wealth and risk that decreases social welfare. Three reasons explain this resulto First, ITR increases the volatility of securities prices, thus making the market more risky; second, it worsens the risk sharing among investors; and, third, it diverts resources from the productive sector of the economy. Further, although I formally establish conditions under which ITR makes society better off, largue that those conditions cannot be used to justify the imposition of this regulation

Structural patterns in complex networks through spectral analysis

The study of some structural properties of networks is introduced from a graph spectral perspective. First, subgraph centrality of nodes is defined and used to classify essential proteins in a proteomic map. This index is then used to produce a method that allows the identification of superhomogeneous networks. At the same time this method classify non-homogeneous network into three universal classes of structure. We give examples of these classes from networks in different real-world scenarios. Finally, a communicability function is studied and showed as an alternative for defining communities in complex networks. Using this approach a community is unambiguously defined and an algorithm for its identification is proposed and exemplified in a real-world network

Communicability in temporal networks

A first-principles approach to quantify the communicability between pairs of nodes in temporal networks is proposed. It corresponds to the imaginary-time propagator of a quantum random walk in the temporal network, which accounts for unique structural and temporal characteristics of both streaming and nonstreaming temporal networks. The influence of the system's temperature on the perdurability of information and how the communicability identifies patterns of communication hidden in the temporal and topological structure of the networks are also studied for synthetic and real-world systems