The centrality of vertices has been a key issue in network analysis. For unweighted networks where edges are just present or absent and have no weight attached, many centrality measures have beenâ€¦ (More)

The odd-girth of a graph is the length of a shortest odd circuit. A conjecture by Pavol Hell about circular coloring is solved in this article by showing that there is a function f( ) for each : 0 <â€¦ (More)

Let G be a simple graph with average degree . d and maximum degree . It is proved, in this paper that G is not critical if . d6 6 and Â¿ 8, or . d6 20 3 and Â¿ 9. This result generalizes earlierâ€¦ (More)

It was conjectured by Tutte that every 4-edge-connected graph admits a nowherezero 3-flow. In this paper, we give a complete characterization of graphs whose squares admit nowhere-zero 3-flows andâ€¦ (More)

It is proved in this paper that every bipartite graphic sequence with the minimum degree Î´ â‰¥ 2 has a realization that admits a nowhere-zero 4-flow. This result implies a conjecture originallyâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2011

In many social networks, there is a high correlation between the similarity of actors and the existence of relationships between them. This paper introduces a model of network evolution where actorsâ€¦ (More)