Here I have collected a number of live models I have written or contributed to. You will find more related live models here: CMOL:models, and here: well-formed.eigenfactor.org.

We have developed the map generator to make it easier for you to simplify and highlight important structures in your networks with the map equation. When you load your weighted or unweighted, directed or undirected network in Pajek format into the applet, the map generator clusters the network based on the map equation and generates a map for you to customize and save as a pdf file.

Martin Rosvall, Daniel Axelsson, and Carl T. Bergstrom, The map equation, [arXiv:0906.1405]

In this dynamic visualization, we explore the duality between finding community structure in networks and minimizing the description length of a random walker on a network. For a given network partition M, the map equation specifies the theoretical limit L(M) of how concisely we can describe the trajectory of this random walk. With a random walk as a proxy for real flow, minimizing the map equation over all possible network partitions reveals important aspects of network structure with respect to the dynamics on the network

Martin Rosvall, Daniel Axelsson, and Carl T. Bergstrom, The map equation, [arXiv:0906.1405]

Social networks represent communication channels and therefore also limits on information access in a society. The applet considers agents who try to bypass these information constraints, driving an ever-changing social network. The model emphasizes communication barriers in the system as the driving force behind group formation.

Martin Rosvall and Kim Sneppen, Reinforced communication and social navigation generate groups in model networks, Phys. Rev. E 79, 026111 (2009). [arXiv:0809.4803]

We map large networks by decomposing the myriad nodes and links into modules or communities, and then identifying the patterns of flow between these modules. Our approach originates within coding theory; we aim to design a code that provides a compressed description of the information flow on the network.

Martin Rosvall and Carl T. Bergstrom, Maps of information flow reveal community structure in complex networks, PNAS 105, 1118 (2008). [arXiv:0707.0609]

Is the number of triangles large or small? The shortest paths short or long? The only way to find out is to compare with a proper null model — a randomized counterpart of the network. This interactive applet makes it easy to make this comparison and to capture the effect different network topologies have on basic network measures, as well as the effect of the addition and removal of individual links.

Martin Rosvall, Information horizons in a complex world.

Social groups with widely different music tastes, political convictions, and religious beliefs emerge and disappear on scales from extreme subcultures to mainstream mass-cultures. Several positive feedback mechanisms drive the diversity of beliefs in social systems. Some of these mechanisms can be analyzed in terms of a hugely simplified model of a dynamic network that incorporates basic feedback between information assembly through communication and the formation of social connections.

Martin Rosvall and Kim Sneppen, Dynamics of opinions and social structures [arXiv:0708.0368]

We examine the co-evolution of bacteria and virulent and temperate phages in a network model where nodes are whole strains of bacteria and phages. This corresponds to a coarse graining of speciations and extinctions on the strain level, ignoring population numbers. Instead, basic features of the ecological interactions are incorporated into the model in the form of extinction probabilities that depend on interaction strengths.

Martin Rosvall, Ian B. Dodd, Sandeep Krishna, and Kim Sneppen, Network models of phage-bacteria coevolution, Phys. Rev. E 74, 066105 (2006). [q-bio.PE/0609031]

We make simple models of our surrounding world using the assumption that the complicatedness of the world is an illusion. This applet exemplifies this approach by showing that simple rules can give rise to complex behavior. It also illustrates that the information horizon of the modeled birds is connected to development of cooperative behavior, which here takes the form of flock behavior. The information horizon aspect of the applet is complementary to the applet on the interplay between communication and social structure. See, for example, the applet Modeling the origin of interest groups.

We take the model in "Self-Assembling of Information in Networks" one step further and give the agents a social mobility. The agents can thereby get new acquaintances to meet different interests. The model opens the study of interplay between communication activity/habits and the emergence of social structure.

Martin Rosvall and Kim Sneppen, Modeling self-organization of communication and topology in social networks, Europhys. Lett. 74, 1109 (2006). [physics/0512105]

We show that it is possible to build a reliable perception of the whole through repeated small talks. We simply let agents remember the acquaintances that provided the newest information about other agents together with the age of this information.

Martin Rosvall and Kim Sneppen, Self-assembly of information in networks, Europhys. Lett. 74, 1109 (2006). [physics/0603218]

Navigation is a challenging problem for everyday life. The problem arises because the amount of available information typically is limited and often is insufficient. Here we abstract this problem to be navigation between a source and a target on different networks.

Martin Rosvall, Petter Minnhagen, and Kim Sneppen, Navigating networks with limited information, Phys. Rev. E 71, 066111 (2005). [cond-mat/0412051]

One way to interpret this merging model of a bipartite network is to consider the nodes as sunspots and the links as the associated magnetic field-lines in the solar atmosphere. Two sunspots of the same polarity merge to a larger sunspot, and when two sunspots of different polarity merge, the magnetic field-lines annihilate and energy is released.

Kim Sneppen, Martin Rosvall, Ala Trusina, and Petter Minnhagen, A simple model for self organization of bipartite networks, Europhys. Lett. 67, 349 (2004). [nlin.AO/0403005]

Merging or aggregation is a dynamic process in many systems and it gives rise to fractal size-distributions. For example, companies, the autonomous system of the Internet and the sun activity of magnetic field lines reconnections are networks that undergo processes that resemble the merging process.

Petter Minnhagen, Martin Rosvall, Kim Sneppen, and Ala Trusina, Self-organization of structures and networks from merging and small-scale fluctuations, Physica A 340, 725 (2004). [cond-mat/0406752]

Speciation and extinction in evolution, modeled in a coarse-grained 1-dimensional ecosystem. Species in the ecosystem do not suffer extinction independently of each other. The overall macroevolutionary pattern supports cooperativity, even on the scale of the global ecosystem.

Per Bak and Kim Sneppen, Punctuated equilibrium and criticality in a simple model of evolution, Phys. Rev. Lett. 69, 3539 (1993)

In a society, the information horizon is set by each individual's social contacts, which in turn are a part of the global network of human communication. One simple goal for individuals is to be central. Thus we model a society where players try to be as close as possible to everybody else by moving their social connections. Local communication gives rise to global organization.

Martin Rosvall and Kim Sneppen, Modeling dynamics of information networks, Phys. Rev. Lett. 91, 178701 (2003). [cond-mat/0308399]