Limits...
Understanding mobility in a social petri dish.

Szell M, Sinatra R, Petri G, Thurner S, Latora V - Sci Rep (2012)

Bottom Line: We find that the motion of individuals is not only constrained by physical distances, but also strongly shaped by the presence of socio-economic areas.These regions can be recovered perfectly by community detection methods solely based on the measured human dynamics.Moreover, we uncover that long-term memory in the time-order of visited locations is the essential ingredient for modeling the trajectories.

View Article: PubMed Central - PubMed

Affiliation: Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria.

ABSTRACT
Despite the recent availability of large data sets on human movements, a full understanding of the rules governing motion within social systems is still missing, due to incomplete information on the socio-economic factors and to often limited spatio-temporal resolutions. Here we study an entire society of individuals, the players of an online-game, with complete information on their movements in a network-shaped universe and on their social and economic interactions. Such a "socio-economic laboratory" allows to unveil the intricate interplay of spatial constraints, social and economic factors, and patterns of mobility. We find that the motion of individuals is not only constrained by physical distances, but also strongly shaped by the presence of socio-economic areas. These regions can be recovered perfectly by community detection methods solely based on the measured human dynamics. Moreover, we uncover that long-term memory in the time-order of visited locations is the essential ingredient for modeling the trajectories.

Show MeSH
Extracting communities from network topology and from mobility patterns.(a) The adjacency matrix A of the universe network, (b) the matrix D of shortest path distances, and (c) the matrix M of transition counts of player jumps. Each of the three matrices contains 400 × 400 entries, whose values are colour-coded. Sector IDs are ordered by cluster, resulting in the block-diagonal form of the three matrices. We have used modularity-optimization algorithms to extract community structures from the information encoded in the three matrices. Different node colours represent the different communities found, while the 20 different colour-shaded areas indicate the predefined socio-economic clusters as in Fig. 1. The displayed Fowlkes and Mallows index  quantifies the overlap of the detected communities with the predefined clusters. The closer  is to 1, the better the match, see Supplementary Section S4. (d) Although information contained in the adjacency matrix A allows to find 18 communities, a number close to the real number of clusters, the communities extracted do not correspond to the underlying colour-shades areas (). (e) Extracting communities from the distance matrix D only results in 6 different groups (). (f) The 23 communities detected using the transition count matrix M reproduce almost perfectly the real socio-economic clusters (), with only a few mismatched nodes detected as additional clusters. For more measures quantifying the match of communities, see Supplementary Table II.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3375635&req=5

f4: Extracting communities from network topology and from mobility patterns.(a) The adjacency matrix A of the universe network, (b) the matrix D of shortest path distances, and (c) the matrix M of transition counts of player jumps. Each of the three matrices contains 400 × 400 entries, whose values are colour-coded. Sector IDs are ordered by cluster, resulting in the block-diagonal form of the three matrices. We have used modularity-optimization algorithms to extract community structures from the information encoded in the three matrices. Different node colours represent the different communities found, while the 20 different colour-shaded areas indicate the predefined socio-economic clusters as in Fig. 1. The displayed Fowlkes and Mallows index quantifies the overlap of the detected communities with the predefined clusters. The closer is to 1, the better the match, see Supplementary Section S4. (d) Although information contained in the adjacency matrix A allows to find 18 communities, a number close to the real number of clusters, the communities extracted do not correspond to the underlying colour-shades areas (). (e) Extracting communities from the distance matrix D only results in 6 different groups (). (f) The 23 communities detected using the transition count matrix M reproduce almost perfectly the real socio-economic clusters (), with only a few mismatched nodes detected as additional clusters. For more measures quantifying the match of communities, see Supplementary Table II.

Mentions: Mobility patterns are influenced by the presence of the socio-economic regions in the network, highlighted in colours in Fig. 1. The typical situation is illustrated in Fig. 3 (a), with jumps within the same cluster being preferred to jumps between sectors in different clusters. In order to quantify this effect, we report in Fig. 3 (b), blue circles, the observed number of jumps of length d within the same cluster, divided by the total number of jumps of length d. This ratio is a decreasing function of the distance d, and reaches zero at d = 12, since no sectors at such distance do belong to the same cluster. As a model we report the fraction of sector pairs at distance d which belong to the same cluster, see red squares in the same figure. The significant discrepancy between the two curves indicates that players indeed tend to avoid crossing the borders between clusters. For example, a jump of length d = 8 from one sector to another sector in the same cluster is expected only in 3% of the cases, while it is observed in about 20% of the cases. Now, the propensity of a player to spend long time periods within the same cluster might be simply related to the topology of the network, as in the case of random walkers whose motions are constrained on graphs with strong community structures34. Nodes belonging to the same cluster are in fact either directly connected or are at short distance from one another. This proximity is reflected in the block-diagonal structure of the adjacency matrix A and of the distance matrix D, respectively shown in Fig. 4 (a) and (b). We have therefore checked whether the presence of the socio-economic clusters originally introduced by the developers of the game can be derived solely from the structure of the network. For this reason we adopted standard community detection methods based on the adjacency and on the distance matrix3536. The results, reported respectively in Fig. 4 (d) and (e), show that detected communities deviate significantly from the clusters, implying that in our online world the socio-economic regions cannot be recovered merely from topological features. In comparison we considered the player transition count matrix M, shown in Fig. 4 (c), which displays a similar block-diagonal structure as A and D, but with the qualitative difference that it contains dynamic information on the system. Figure 4 (f) shows that community detection methods applied to the transition count matrix M reveal almost perfectly all the socio-economic areas of the universe. This finding demonstrates that mobility patterns contain fundamental information on the socio-economic constraints present in a social system. Therefore, a community detection algorithm applied to raw mobility information, as the one proposed here, is able to extract the underlying socio-economic features, which are instead invisible to methods based solely on topology. For a detailed treatment of adopted community detection methods and measures see Supplementary Section S4, Supplementary Table II and Supplementary Figs. 4 and 5.


Understanding mobility in a social petri dish.

Szell M, Sinatra R, Petri G, Thurner S, Latora V - Sci Rep (2012)

Extracting communities from network topology and from mobility patterns.(a) The adjacency matrix A of the universe network, (b) the matrix D of shortest path distances, and (c) the matrix M of transition counts of player jumps. Each of the three matrices contains 400 × 400 entries, whose values are colour-coded. Sector IDs are ordered by cluster, resulting in the block-diagonal form of the three matrices. We have used modularity-optimization algorithms to extract community structures from the information encoded in the three matrices. Different node colours represent the different communities found, while the 20 different colour-shaded areas indicate the predefined socio-economic clusters as in Fig. 1. The displayed Fowlkes and Mallows index  quantifies the overlap of the detected communities with the predefined clusters. The closer  is to 1, the better the match, see Supplementary Section S4. (d) Although information contained in the adjacency matrix A allows to find 18 communities, a number close to the real number of clusters, the communities extracted do not correspond to the underlying colour-shades areas (). (e) Extracting communities from the distance matrix D only results in 6 different groups (). (f) The 23 communities detected using the transition count matrix M reproduce almost perfectly the real socio-economic clusters (), with only a few mismatched nodes detected as additional clusters. For more measures quantifying the match of communities, see Supplementary Table II.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3375635&req=5

f4: Extracting communities from network topology and from mobility patterns.(a) The adjacency matrix A of the universe network, (b) the matrix D of shortest path distances, and (c) the matrix M of transition counts of player jumps. Each of the three matrices contains 400 × 400 entries, whose values are colour-coded. Sector IDs are ordered by cluster, resulting in the block-diagonal form of the three matrices. We have used modularity-optimization algorithms to extract community structures from the information encoded in the three matrices. Different node colours represent the different communities found, while the 20 different colour-shaded areas indicate the predefined socio-economic clusters as in Fig. 1. The displayed Fowlkes and Mallows index quantifies the overlap of the detected communities with the predefined clusters. The closer is to 1, the better the match, see Supplementary Section S4. (d) Although information contained in the adjacency matrix A allows to find 18 communities, a number close to the real number of clusters, the communities extracted do not correspond to the underlying colour-shades areas (). (e) Extracting communities from the distance matrix D only results in 6 different groups (). (f) The 23 communities detected using the transition count matrix M reproduce almost perfectly the real socio-economic clusters (), with only a few mismatched nodes detected as additional clusters. For more measures quantifying the match of communities, see Supplementary Table II.
Mentions: Mobility patterns are influenced by the presence of the socio-economic regions in the network, highlighted in colours in Fig. 1. The typical situation is illustrated in Fig. 3 (a), with jumps within the same cluster being preferred to jumps between sectors in different clusters. In order to quantify this effect, we report in Fig. 3 (b), blue circles, the observed number of jumps of length d within the same cluster, divided by the total number of jumps of length d. This ratio is a decreasing function of the distance d, and reaches zero at d = 12, since no sectors at such distance do belong to the same cluster. As a model we report the fraction of sector pairs at distance d which belong to the same cluster, see red squares in the same figure. The significant discrepancy between the two curves indicates that players indeed tend to avoid crossing the borders between clusters. For example, a jump of length d = 8 from one sector to another sector in the same cluster is expected only in 3% of the cases, while it is observed in about 20% of the cases. Now, the propensity of a player to spend long time periods within the same cluster might be simply related to the topology of the network, as in the case of random walkers whose motions are constrained on graphs with strong community structures34. Nodes belonging to the same cluster are in fact either directly connected or are at short distance from one another. This proximity is reflected in the block-diagonal structure of the adjacency matrix A and of the distance matrix D, respectively shown in Fig. 4 (a) and (b). We have therefore checked whether the presence of the socio-economic clusters originally introduced by the developers of the game can be derived solely from the structure of the network. For this reason we adopted standard community detection methods based on the adjacency and on the distance matrix3536. The results, reported respectively in Fig. 4 (d) and (e), show that detected communities deviate significantly from the clusters, implying that in our online world the socio-economic regions cannot be recovered merely from topological features. In comparison we considered the player transition count matrix M, shown in Fig. 4 (c), which displays a similar block-diagonal structure as A and D, but with the qualitative difference that it contains dynamic information on the system. Figure 4 (f) shows that community detection methods applied to the transition count matrix M reveal almost perfectly all the socio-economic areas of the universe. This finding demonstrates that mobility patterns contain fundamental information on the socio-economic constraints present in a social system. Therefore, a community detection algorithm applied to raw mobility information, as the one proposed here, is able to extract the underlying socio-economic features, which are instead invisible to methods based solely on topology. For a detailed treatment of adopted community detection methods and measures see Supplementary Section S4, Supplementary Table II and Supplementary Figs. 4 and 5.

Bottom Line: We find that the motion of individuals is not only constrained by physical distances, but also strongly shaped by the presence of socio-economic areas.These regions can be recovered perfectly by community detection methods solely based on the measured human dynamics.Moreover, we uncover that long-term memory in the time-order of visited locations is the essential ingredient for modeling the trajectories.

View Article: PubMed Central - PubMed

Affiliation: Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria.

ABSTRACT
Despite the recent availability of large data sets on human movements, a full understanding of the rules governing motion within social systems is still missing, due to incomplete information on the socio-economic factors and to often limited spatio-temporal resolutions. Here we study an entire society of individuals, the players of an online-game, with complete information on their movements in a network-shaped universe and on their social and economic interactions. Such a "socio-economic laboratory" allows to unveil the intricate interplay of spatial constraints, social and economic factors, and patterns of mobility. We find that the motion of individuals is not only constrained by physical distances, but also strongly shaped by the presence of socio-economic areas. These regions can be recovered perfectly by community detection methods solely based on the measured human dynamics. Moreover, we uncover that long-term memory in the time-order of visited locations is the essential ingredient for modeling the trajectories.

Show MeSH