Ghetto of Venice: Access to the Target Node and the Random Target Access Time

Random walks defined on undirected graphs assign the absolute scores to all nodes based on the quality of path they provide for random walkers. In city space syntax, the notion of segregation acquires a statistical interpretation with respect to random walks. We analyze the spatial network of Venetian canals and detect its most segregated part which can be identified with canals adjacent to the Ghetto of Venice.Comment: 14 pages, 3 figure

Intelligibility and First Passage Times In Complex Urban Networks

Topology of urban environments can be represented by means of graphs. We explore the graph representations of several compact urban patterns by random walks. The expected time of recurrence and the expected first passage time to a node scales apparently linearly in all urban patterns we have studied In space syntax theory, a positive relation between the local property of a node (qualified by connectivity or by the recurrence time) and the global property of the node (estimated in our approach by the first passage time to it) is known as intelligibility. Our approach based on random walks allows to extend the notion of intelligibility onto the entire domain of complex networks and graph theory.Comment: 19 pages, 4 figures, English UK, the Harvard style reference

The "Cameo Principle" and the Origin of Scale-Free Graphs in Social Networks

We formulate a simple edge generation rule based on an inverse like mass action principle for random graphs over a structured vertex set. We show that under very weak assumptions on the structure generating distribution we obtain a scale free distribution for the degree. We furthermore introduce and study a "my friends are your friends" local search principle which makes the clustering coefficient large.Comment: 17 pages, Late

Random Walks Estimate Land Value

Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time to a place correlates with assessed value of land in that. The method accounting the average number of random turns at junctions on the way to reach any particular place in the city from various starting points could be used to identify isolated neighborhoods in big cities with a complex web of roads, walkways and public transport systems