Game Theoretic Formation of a Centrality Based Network

We model the formation of networks as a game where players aspire to maximize their own centrality by increasing the number of other players to which they are path-wise connected, while simultaneously incurring a cost for each added adjacent edge. We simulate the interactions between players using an algorithm that factors in rational strategic behavior based on a common objective function. The resulting networks exhibit pairwise stability, from which we derive necessary stable conditions for specific graph topologies. We then expand the model to simulate non-trivial games with large numbers of players. We show that using conditions necessary for the stability of star topologies we can induce the formation of hub players that positively impact the total welfare of the network.Comment: Submitted to 2012 ASE Social Informatics Conferenc

Efficient computation of the Shapley value for game-theoretic network centrality

The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo

Offloading Content with Self-organizing Mobile Fogs

Mobile users in an urban environment access content on the internet from different locations. It is challenging for the current service providers to cope with the increasing content demand from a large number of collocated mobile users. In-network caching to offload content at nodes closer to users alleviate the issue, though efficient cache management is required to find out who should cache what, when and where in an urban environment, given nodes limited computing, communication and caching resources. To address this, we first define a novel relation between content popularity and availability in the network and investigate a node's eligibility to cache content based on its urban reachability. We then allow nodes to self-organize into mobile fogs to increase the distributed cache and maximize content availability in a cost-effective manner. However, to cater rational nodes, we propose a coalition game for the nodes to offer a maximum "virtual cache" assuming a monetary reward is paid to them by the service/content provider. Nodes are allowed to merge into different spatio-temporal coalitions in order to increase the distributed cache size at the network edge. Results obtained through simulations using realistic urban mobility trace validate the performance of our caching system showing a ratio of 60-85% of cache hits compared to the 30-40% obtained by the existing schemes and 10% in case of no coalition

Social networks: Prestige, centrality, and influence (Invited paper)

We deliver a short overview of di erent centrality measures and influence concepts in social networks, and present the relation-algebraic approach to the concepts of power and influence. First, we briefly discuss four kinds of measures of centrality: the ones based on degree, closeness, betweenness, and the eigenvector-related measures. We consider centrality of a node and of a network. Moreover, we give a classi cation of the centrality measures based on a topology of network flows. Furthermore, we present a certain model of influence in a social network and discuss some applications of relation algebra and RelView to this model.social network ; centrality ; prestige ; influence ; relation algebra ; RelView

A Content-based Centrality Metric for Collaborative Caching in Information-Centric Fogs

Information-Centric Fog Computing enables a multitude of nodes near the end-users to provide storage, communication, and computing, rather than in the cloud. In a fog network, nodes connect with each other directly to get content locally whenever possible. As the topology of the network directly influences the nodes' connectivity, there has been some work to compute the graph centrality of each node within that network topology. The centrality is then used to distinguish nodes in the fog network, or to prioritize some nodes over others to participate in the caching fog. We argue that, for an Information-Centric Fog Computing approach, graph centrality is not an appropriate metric. Indeed, a node with low connectivity that caches a lot of content may provide a very valuable role in the network. To capture this, we introduce acontent-based centrality (CBC) metric which takes into account how well a node is connected to the content the network is delivering, rather than to the other nodes in the network. To illustrate the validity of considering content-based centrality, we use this new metric for a collaborative caching algorithm. We compare the performance of the proposed collaborative caching with typical centrality based, non-centrality based, and non-collaborative caching mechanisms. Our simulation implements CBC on three instances of large scale realistic network topology comprising 2,896 nodes with three content replication levels. Results shows that CBC outperforms benchmark caching schemes and yields a roughly 3x improvement for the average cache hit rate

Assortative Mixing Equilibria in Social Network Games

It is known that individuals in social networks tend to exhibit homophily (a.k.a. assortative mixing) in their social ties, which implies that they prefer bonding with others of their own kind. But what are the reasons for this phenomenon? Is it that such relations are more convenient and easier to maintain? Or are there also some more tangible benefits to be gained from this collective behaviour? The current work takes a game-theoretic perspective on this phenomenon, and studies the conditions under which different assortative mixing strategies lead to equilibrium in an evolving social network. We focus on a biased preferential attachment model where the strategy of each group (e.g., political or social minority) determines the level of bias of its members toward other group members and non-members. Our first result is that if the utility function that the group attempts to maximize is the degree centrality of the group, interpreted as the sum of degrees of the group members in the network, then the only strategy achieving Nash equilibrium is a perfect homophily, which implies that cooperation with other groups is harmful to this utility function. A second, and perhaps more surprising, result is that if a reward for inter-group cooperation is added to the utility function (e.g., externally enforced by an authority as a regulation), then there are only two possible equilibria, namely, perfect homophily or perfect heterophily, and it is possible to characterize their feasibility spaces. Interestingly, these results hold regardless of the minority-majority ratio in the population. We believe that these results, as well as the game-theoretic perspective presented herein, may contribute to a better understanding of the forces that shape the groups and communities of our society