Petter Holme

We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph. For each case of attacks on vertices and edges, four different attacking strategies are used: removals by the descending or

We extend the standard scale-free network model to include a "triad formation step." We analyze the geometric properties of networks generated by this algorithm both analytically and by numerical calculations, and find that our model possesses the same characteristics as the standard scale-free networks such as the power-law degree distribution and the small average geodesic length, but with the high clustering at the same time. In our model, the clustering coefficient is also shown to be tunabl

Models of the convergence of opinion in social systems have been the subject of considerable recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquainta

Supplementary material is available at http://www.tp.umu.se/forskning/networks/meta/

Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. Among other things we conclude that geographically embedded transportation networks have a strong core-perip

We study evolving networks based on the Barabási-Albert scale-free network model with vertices sensitive to overload breakdown. The load of a vertex is defined as the betweenness centrality of the vertex. Two cases of load limitation are considered, corresponding to the fact that the average number of connections per vertex is increasing with the network's size ("extrinsic communication activity"), or that it is constant ("intrinsic communication activity"). Avalanchelike breakdowns for both loa

We use real-world contact sequences, time-ordered lists of contacts from one person to another, to study how fast information or disease can spread across network of contacts. Specifically we measure the reachability time--the average shortest time for a series of contacts to spread information between a reachable pair of vertices (a pair where a chain of contacts exists leading from one person to the other)--and the reachability ratio--the fraction of reachable vertex pairs. These measures are

We investigate growing networks based on Barabási and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. The load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, like the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown i

Are scale-free networks rare or universal? Important or not? We present the recent research about degree distributions of networks. This is a controversial topic, but, we argue, with some adjustments of the terminology, it does not have to be.

We study how a fraction of a population should be vaccinated to most efficiently top epidemics. We argue that only local information (about the neighborhood of specific vertices) is usable in practice, and hence we consider only local vaccination strategies. The efficiency of the vaccination strategies is investigated with both static and dynamical measures. Among other things we find that the most efficient strategy for many real-world situations is to iteratively vaccinate the neighbor of the

Systems with two types of agents with a preference for heterophilous interaction produce networks that are more or less close to bipartite. We propose two measures quantifying the notion of bipartivity. The two measures-one well known and natural, but computationally intractable, and the other computationally less complex, but also less intuitive-are examined on model networks that continuously interpolate between bipartite graphs and graphs with many odd circuits. We find that the bipartivity m

Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated