Modeling self-organization of communication and topology in social networks

This paper introduces a model of self-organization between communication and topology in social networks, with a feedback between different communication habits and the topology. To study this feedback, we let agents communicate to build a perception of a network and use this information to create strategic links. We observe a narrow distribution of links when the communication is low and a system with a broad distribution of links when the communication is high. We also analyze the outcome of chatting, cheating, and lying, as strategies to get better access to information in the network. Chatting, although only adopted by a few agents, gives a global gain in the system. Contrary, a global loss is inevitable in a system with too many liarsComment: 6 pages 7 figures, Java simulation available at http://cmol.nbi.dk/models/inforew/inforew.htm

Spectral centrality measures in complex networks

Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes based on their topological importance within a graph. Here we review and compare centrality measures based on spectral properties of graph matrices. We shall focus on PageRank, eigenvector centrality and the hub/authority scores of HITS. We derive simple relations between the measures and the (in)degree of the nodes, in some limits. We also compare the rankings obtained with different centrality measures.Comment: 11 pages, 10 figures, 5 tables. Final version published in Physical Review

Superlinear Scaling for Innovation in Cities

Superlinear scaling in cities, which appears in sociological quantities such as economic productivity and creative output relative to urban population size, has been observed but not been given a satisfactory theoretical explanation. Here we provide a network model for the superlinear relationship between population size and innovation found in cities, with a reasonable range for the exponent.Comment: 5 pages, 5 figures, 1 table, submitted to Phys. Rev. E; references corrected; figures corrected, references and brief discussion adde

Paradoxes in Fair Computer-Aided Decision Making

Computer-aided decision making--where a human decision-maker is aided by a computational classifier in making a decision--is becoming increasingly prevalent. For instance, judges in at least nine states make use of algorithmic tools meant to determine "recidivism risk scores" for criminal defendants in sentencing, parole, or bail decisions. A subject of much recent debate is whether such algorithmic tools are "fair" in the sense that they do not discriminate against certain groups (e.g., races) of people. Our main result shows that for "non-trivial" computer-aided decision making, either the classifier must be discriminatory, or a rational decision-maker using the output of the classifier is forced to be discriminatory. We further provide a complete characterization of situations where fair computer-aided decision making is possible

Solution for the properties of a clustered network

We study Strauss's model of a network with clustering and present an analytic mean-field solution which is exact in the limit of large network size. Previous computer simulations have revealed a degenerate region in the model's parameter space in which triangles of adjacent edges clump together to form unrealistically dense subgraphs, and perturbation calculations have been found to break down in this region at all orders. Our analytic solution shows that this region corresponds to a classic symmetry-broken phase and that the onset of the degeneracy corresponds to a first-order phase transition in the density of the network.Comment: 5 pages, 2 figure

Exact solutions for models of evolving networks with addition and deletion of nodes

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied. In the real world, however, many networks, including the web, not only add vertices but also lose them. Here we formulate models of the time evolution of such networks and give exact solutions for a number of cases of particular interest. For the case of net growth and so-called preferential attachment -- in which newly appearing vertices attach to previously existing ones in proportion to vertex degree -- we show that the resulting networks have power-law degree distributions, but with an exponent that diverges as the growth rate vanishes. We conjecture that the low exponent values observed in real-world networks are thus the result of vigorous growth in which the rate of addition of vertices far exceeds the rate of removal. Were growth to slow in the future, for instance in a more mature future version of the web, we would expect to see exponents increase, potentially without bound.Comment: 9 pages, 3 figure

Degree Distribution of Competition-Induced Preferential Attachment Graphs

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment random graph models with upper cutoffs. This is the first explanation of how preferential attachment can arise from a more basic underlying mechanism of local competition. We rigorously determine the degree distribution for the family of random graph models, showing that it obeys a power law up to a finite threshold and decays exponentially above this threshold. We also rigorously analyze a generalized version of our graph process, with two natural parameters, one corresponding to the cutoff and the other a ``fertility'' parameter. We prove that the general model has a power-law degree distribution up to a cutoff, and establish monotonicity of the power as a function of the two parameters. Limiting cases of the general model include the standard preferential attachment model without cutoff and the uniform attachment model.Comment: 24 pages, one figure. To appear in the journal: Combinatorics, Probability and Computing. Note, this is a long version, with complete proofs, of the paper "Competition-Induced Preferential Attachment" (cond-mat/0402268

Finding local community structure in networks

Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time. This algorithm runs in time O(d*k^2) for general graphs when $d$ is the mean degree and k is the number of vertices to be explored. For graphs where exploring a new vertex is time-consuming, the running time is linear, O(k). We show that on computer-generated graphs this technique compares favorably to algorithms that require global knowledge. We also use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer and show the existence of mesoscopic structure.Comment: 7 pages, 6 figure

Fusing Data with Correlations

Many applications rely on Web data and extraction systems to accomplish knowledge-driven tasks. Web information is not curated, so many sources provide inaccurate, or conflicting information. Moreover, extraction systems introduce additional noise to the data. We wish to automatically distinguish correct data and erroneous data for creating a cleaner set of integrated data. Previous work has shown that a na\"ive voting strategy that trusts data provided by the majority or at least a certain number of sources may not work well in the presence of copying between the sources. However, correlation between sources can be much broader than copying: sources may provide data from complementary domains (\emph{negative correlation}), extractors may focus on different types of information (\emph{negative correlation}), and extractors may apply common rules in extraction (\emph{positive correlation, without copying}). In this paper we present novel techniques modeling correlations between sources and applying it in truth finding.Comment: Sigmod'201

Modeling Dynamics of Information Networks

We propose an information-based model for network dynamics in which imperfect information leads to networks where the different vertices have widely different number of edges to other vertices, and where the topology has hierarchical features. The possibility to observe scale free networks is linked to a minimally connected system where hubs remain dynamic.Comment: 4 pages, 5 figures; changed content and new fig