About some robustness and complexity properties of G-graphs networks

Given a finite group G and a set S ⊂ G, we consider the different cosets of each cyclic group ⟨s⟩ with s ∈ S. Then the G-graph Φ(G, S) associated with G and S can be defined as the intersection graph of all these cosets. These graphs were introduced in Bretto and Faisant (2005) as an alternative to Cayley graphs: they still have strong regular properties but a more flexible structure. We investigate here some of their robustness properties (connectivity and vertex/edge-transitivity) recognized as important issues in the domain of network design. In particular, we exhibit some cases where G-graphs are optimally connected, i.e. their edge and vertex-connectivity are both equal to the minimum degree. Our main result concerns the case of a G-graph associated with an abelian group and its canonical base S, which is shown to be optimally connected. We also provide a combinatorial characterization for this class as clique graphs of Cartesian products of complete graphs and we show that it can be recognized in polynomial time. These results motivate future researches in two main directions: revealing new classes of optimally connected G-graphs and investigating the complexity of their recognitio

Robustness: a New Form of Heredity Motivated by Dynamic Networks

We investigate a special case of hereditary property in graphs, referred to as {\em robustness}. A property (or structure) is called robust in a graph $G$ if it is inherited by all the connected spanning subgraphs of $G$. We motivate this definition using two different settings of dynamic networks. The first corresponds to networks of low dynamicity, where some links may be permanently removed so long as the network remains connected. The second corresponds to highly-dynamic networks, where communication links appear and disappear arbitrarily often, subject only to the requirement that the entities are temporally connected in a recurrent fashion ({\it i.e.} they can always reach each other through temporal paths). Each context induces a different interpretation of the notion of robustness. We start by motivating the definition and discussing the two interpretations, after what we consider the notion independently from its interpretation, taking as our focus the robustness of {\em maximal independent sets} (MIS). A graph may or may not admit a robust MIS. We characterize the set of graphs \forallMIS in which {\em all} MISs are robust. Then, we turn our attention to the graphs that {\em admit} a robust MIS (\existsMIS). This class has a more complex structure; we give a partial characterization in terms of elementary graph properties, then a complete characterization by means of a (polynomial time) decision algorithm that accepts if and only if a robust MIS exists. This algorithm can be adapted to construct such a solution if one exists

Contrasting Views of Complexity and Their Implications For Network-Centric Infrastructures

There exists a widely recognized need to better understand and manage complex “systems of systems,” ranging from biology, ecology, and medicine to network-centric technologies. This is motivating the search for universal laws of highly evolved systems and driving demand for new mathematics and methods that are consistent, integrative, and predictive. However, the theoretical frameworks available today are not merely fragmented but sometimes contradictory and incompatible. We argue that complexity arises in highly evolved biological and technological systems primarily to provide mechanisms to create robustness. However, this complexity itself can be a source of new fragility, leading to “robust yet fragile” tradeoffs in system design. We focus on the role of robustness and architecture in networked infrastructures, and we highlight recent advances in the theory of distributed control driven by network technologies. This view of complexity in highly organized technological and biological systems is fundamentally different from the dominant perspective in the mainstream sciences, which downplays function, constraints, and tradeoffs, and tends to minimize the role of organization and design

The Food Web of Potter Cove (Antarctica): complexity, structure and function

Knowledge of the food web structure and complexity are central to better understand ecosystem functioning. A food-web approach includes both species and energy flows among them, providing a natural framework for characterizing species’ ecological roles and the mechanisms through which biodiversity influences ecosystem dynamics. Here we present for the first time a high-resolution food web for a marine ecosystem at Potter Cove (northern Antarctic Peninsula). Eleven food web properties were analyzed in order to document network complexity, structure and topology. We found a low linkage density (3.4), connectance (0.04) and omnivory percentage (45), as well as a short path length (1.8) and a low clustering coefficient (0.08). Furthermore, relating the structure of the food web to its dynamics, an exponential degree distribution (in- and out-links) was found. This suggests that the Potter Cove food web may be vulnerable if the most connected species became locally extinct. For two of the three more connected functional groups, competition overlap graphs imply high trophic interaction between demersal fish and niche specialization according to feeding strategies in amphipods. On the other hand, the prey overlap graph shows also that multiple energy pathways of carbon flux exist across benthic and pelagic habitats in the Potter Cove ecosystem. Although alternative food sources might add robustness to the web, network properties (low linkage density, connectance and omnivory) suggest fragility and potential trophic cascade effects.Fil: Marina, Tomas Ignacio. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Universidad Nacional de Luján. Instituto de Ecología y Desarrollo Sustentable. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Ecología y Desarrollo Sustentable; ArgentinaFil: Salinas, Vanesa Anabella. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Cordone, Georgina Florencia. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Campana, Gabriela Laura. Universidad Nacional de Luján. Instituto de Ecología y Desarrollo Sustentable. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Ecología y Desarrollo Sustentable; Argentina. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Moreira, María Eugenia. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Deregibus, Dolores. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Torre, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; ArgentinaFil: Sahade, Ricardo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; ArgentinaFil: Tatian, Marcos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; ArgentinaFil: Barrera Oro, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales ; ArgentinaFil: De Troch, Marleen. University College Ghent; BélgicaFil: Doyle, Santiago Raúl. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Quartino, Maria Liliana. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Saravia, Leonardo Ariel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Momo, Fernando Roberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Universidad Nacional de Luján. Instituto de Ecología y Desarrollo Sustentable. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Ecología y Desarrollo Sustentable; Argentin

Selection, tinkering and emergence in complex networks: crossing the land of tinkering

Complex biological networks have very different origins than technologic ones. The latter involve extensive design and, as engineered structures, include a high level of optimization. The former involve (in principle) contingency and structural constraints, with new structures being incorporated through tinkering with previously evolved modules or units. However, the observation of the topological features of different biological nets suggests that nature can have a limited repertoire of ”attractors” that essentially optimize communication under some basic constraints of cost and architecture or that allow the biological nets to reach a high degree of homeostasis. Conversely, the topological features exhibited by some technology graphs indicate that tinkering and internal constraints play a key role, in spite of the ”designed” nature of these structures. Previous scenarios suggested to explain the overall trends of evolution are re-analyzed in light of topological patterns.Peer ReviewedPostprint (author's final draft