In　this　paper,　we　study　the　problem　of　data　gathering　with　compressive　sensing　(CS)　in　wireless　sensor　networks　(WSNs).　Unlike　the　conventional　approaches,　which　require　uniform　sampling　in　the　traditional　CS　theory,　we　propose　a　random　walk　algorithm　for　data　gathering　in　WSNs.　However,　such　an　approach　will　conform　to　path　constraints　in　networks　and　result　in　the　non-uniform　selection　of　measurements.　It　is　still　unknown　whether　such　a　non-uniform　method　can　be　used　for　CS　to　recover　sparse　signals　in　WSNs.　In　this　paper,　from　the　perspectives　of　CS　theory　and　graph　theory,　we　provide　mathematical　foundations　to　allow　random　measurements　to　be　collected　in　a　random　walk　based　manner.　We　find　that　the　random　matrix　constructed　from　our　random　walk　algorithm　can　satisfy　the　expansion　property　of　expander　graphs.　The　theoretical　analysis　shows　that　a　k-sparse　signal　can　be　recovered　using　1　minimization　decoding　algorithm　when　it　takes　m　=　O(k　log(n/k))　independent　random　walks　with　the　length　of　each　walk　t　=　O(n/k)　in　a　random　geometric　network　with　n　nodes.　We　also　carry　out　simulations　to　demonstrate　the　effectiveness　of　the　proposed　scheme.　Simulation　results　show　that　our　proposed　scheme　can　significantly　reduce　communication　cost　compared　to　the　conventional　schemes　using　dense　random　projections　and　sparse　random　projections,　indicating　that　our　scheme　can　be　a　more　practical　alternative　for　data　gathering　applications　in　WSNs.　©　2014　IEEE.