Tim Evans

In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes so that nodes may be in more than one community. We do this by making a node partition of the line graph of the original network. In this way we show that any algorithm that produces a partition of nodes can be used to produce a partition of links. We discuss the role of the degree heterogeneity and propose a weighted version of the line graph in order to account for this.

Many complex systems are organized in the form of a network embedded in space. Important examples include the physical Internet infrastructure, road networks, flight connections, brain functional networks, and social networks. The effect of space on network topology has recently come under the spotlight because of the emergence of pervasive technologies based on geolocalization, which constantly fill databases with people's movements and thus reveal their trajectories and spatial behavior. Extracting patterns and regularities from the resulting massive amount of human mobility data requires the development of appropriate tools for uncovering information in spatially embedded networks. In contrast with most works that tend to apply standard network metrics to any type of network, we argue in this paper for a careful treatment of the constraints imposed by space on network topology. In particular, we focus on the problem of community detection and propose a modularity function adapted to spatial networks. We show that it is possible to factor out the effect of space in order to reveal more clearly hidden structural similarities between the nodes. Methods are tested on a large mobile phone network and computer-generated benchmarks where the effect of space has been incorporated.

Abstract The authors raise spatial analysis to a new level of sophistication – and insight – in proposing a mathematical model of ‘imperfect optimisation’ to describe maritime networks. This model encodes, metaphorically, the notion of gravitational attraction between objects in space. The space studied here is the southern Aegean in the Middle Bronze Age, and the objects are the 34 main sites we know about. The ‘gravitation’ in this case is a balance of social forces, expressed by networks with settlements of particular sizes and links of particular strengths. The model can be tweaked by giving different relative importance to the cultivation of local resources or to trade, and to show what happens when a member of the network suddenly disappears.

What was the effect on Late Minoan civilisation of the catastrophic destruction of Akrotiri on Thera (Santorini) by volcanic eruption? Not much, according to the evidence for continuing prosperity on Crete. But the authors mobilise their ingenious mathematical model (published in Antiquity 82: 1009–1024), this time to show that the effects of removing a major port of call could have impacted after an interval, as increased costs of transport gradually led to ever fewer routes and eventual economic collapse.