Graph Annotations in Modeling Complex Network Topologies

The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in such a graph possess some non-trivial internal structure that varies across and differentiates among distinct types of links or nodes. In this work, we abstract such additional information as network annotations. We introduce a network topology modeling framework that treats annotations as an extended correlation profile of a network. Assuming we have this profile measured for a given network, we present an algorithm to rescale it in order to construct networks of varying size that still reproduce the original measured annotation profile. Using this methodology, we accurately capture the network properties essential for realistic simulations of network applications and protocols, or any other simulations involving complex network topologies, including modeling and simulation of network evolution. We apply our approach to the Autonomous System (AS) topology of the Internet annotated with business relationships between ASs. This topology captures the large-scale structure of the Internet. In depth understanding of this structure and tools to model it are cornerstones of research on future Internet architectures and designs. We find that our techniques are able to accurately capture the structure of annotation correlations within this topology, thus reproducing a number of its important properties in synthetically-generated random graphs

Establishing norms with metanorms over interaction topologies

Norms are a valuable means of establishing coherent cooperative behaviour in decentralised systems in which there is no central authority. Axelrod’s seminal model of norm establishment in populations of self-interested individuals provides some insight into the mechanisms needed to support this through the use of metanorms, but considers only limited scenarios and domains. While further developments of Axelrod’s model have addressed some of the limitations, there is still only limited consideration of such metanorm models with more realistic topological configurations. In response, this paper tries to address such limitation by considering its application to different topological structures. Our results suggest that norm establishment is achievable in lattices and small worlds, while such establishment is not achievable in scale-free networks, due to the problematic effects of hubs. The paper offers a solution, first by adjusting the model to more appropriately reflect the characteristics of the problem, and second by offering a new dynamic policy adaptation approach to learning the right behaviour. Experimental results demonstrate that this dynamic policy adaptation overcomes the difficulties posed by the asymmetric distribution of links in scale-free networks, leading to an absence of norm violation, and instead to norm emergence

Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.Comment: To appear in IEEE Trans. Automat. Control; 15 pages, 2 figure

Convention emergence in partially observable topologies

In multi-agent systems it is often desirable for agents to adhere to standards of behaviour that minimise clashes and wasting of (limited) resources. In situations where it is not possible or desirable to dictate these standards globally or via centralised control, convention emergence offers a lightweight and rapid alternative. Placing fixed strategy agents within a population has been shown to facilitate faster convention emergence with some degree of control. Placing these fixed strategy agents at topologically influential locations (such as high-degree nodes) increases their effectiveness. However, finding such influential locations often assumes that the whole network is visible or that it is feasible to inspect the whole network in a computationally practical time, a fact not guaranteed in many real-world scenarios. We present an algorithm, PO-Place, that finds influential nodes given a finite number of network observations. We show that PO-Place finds sets of nodes with similar reach and influence to the set of high-degree nodes and we then compare the performance of PO-Place to degree placement for convention emergence in several real-world topologies